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Cubic surface

In mathematics, a cubic surface is a surface in 3-dimensional space defined by one polynomial equation of degree 3. Cubic surfaces are fundamental examples in algebraic geometry; the theory is simplified by working in projective space rather than affine space, so cubic surfaces are considered in projective 3-space P 3. The theory becomes more uniform by focusing on surfaces over the complex numbers rather than the real numbers. A simple example is the Fermat cubic surface x 3 + y 3 + z 3 + w 3 = 0 in P 3. Many properties of cubic surfaces hold more for del Pezzo surfaces. A central feature of smooth cubic surfaces X over an algebraically closed field is that they are all rational, as shown by Alfred Clebsch in 1866; that is, there is a one-to-one correspondence defined by rational functions between the projective plane P 2 minus a lower-dimensional subset and X minus a lower-dimensional subset. More every irreducible cubic surface over an algebraically closed field is rational unless it is the projective cone over a cubic curve.

In this respect, cubic surfaces are much simpler than smooth surfaces of degree at least 4 in P 3, which are never rational. In characteristic zero, smooth surfaces of degree at least 4 in P 3 are not uniruled. More Clebsch showed that every smooth cubic surface in P 3 over an algebraically closed field is isomorphic to the blow-up of P 2 at 6 points; as a result, every smooth cubic surface over the complex numbers is diffeomorphic to the connected sum C P 2 # 6, where the minus sign refers to a change of orientation. Conversely, the blow-up of P 2 at 6 points is isomorphic to a cubic surface if and only if the points are in general position, meaning that no three points lie on a line and all 6 do not lie on a conic; as a complex manifold, the surface depends on the arrangement of those 6 points. Most proofs of rationality for cubic surfaces start by finding a line on the surface. More Arthur Cayley and George Salmon showed in 1849 that every smooth cubic surface over an algebraically closed field contains 27 lines.

This is a distinctive feature of cubics: a smooth quadric surface is covered by a continuous family of lines, while most surfaces of degree at least 4 in P 3 contain no lines. As the coefficients of a smooth complex cubic surface are varied, the 27 lines move continuously; as a result, a closed loop in the family of smooth cubic surfaces determines a permutation of the 27 lines. The group of permutations of the 27 lines arising this way is called the monodromy group of the family of cubic surfaces. A remarkable 19th-century discovery was that the monodromy group is neither trivial nor the whole symmetric group S 27; this group was recognized as the Weyl group of type E 6, a group generated by reflections on a 6-dimensional real vector space, related to the Lie group E 6 of dimension 78. The same group of order 51840 can be described in combinatorial terms, as the automorphism group of the graph of the 27 lines, with a vertex for each line and an edge whenever two lines meet; this graph was analyzed in the 19th century using subgraphs such as the Schläfli double six configuration.

The complementary graph is known as the Schläfli graph. Many problems about cubic surfaces can be solved using the combinatorics of the E 6 root system. For example, the 27 lines can be identified with the weights of the fundamental representation of the Lie group E 6; the possible sets of singularities that can occur on a cubic surface can be described in terms of subsystems of the E 6 root system. One explanation for this connection is that the E 6 lattice arises as the orthogonal complement to the anticanonical class − K X in the Picard group Pic ⁡ ≅ Z 7, with its intersection form. For a smooth complex cubic surface, the Picard lattice can

Christ of the Abyss

Christ of the Abyss is a submerged bronze statue of Jesus Christ by Guido Galletti, the original cast of, located in the Mediterranean Sea, off San Fruttuoso, between Camogli and Portofino on the Italian Riviera. Various other casts of the statue are located in other places worldwide, in underwater locations and museums; the original clay positive, minus the arms, was located in a foundry in 1993. The arms were found and attached, but not the hands, which had to be replaced; the reconfigured clay sculpture is now on display at the National Museum of Underwater Activities in Ravenna, Italy. The original bronze statue was placed in the Mediterranean Sea on 22 August 1954, at 17 metres depth, stands 2.5 metres tall. It was sculpted based on an idea of Italian diving instructor Duilio Marcante; the statue was placed near the spot where Dario Gonzatti, the first Italian to use SCUBA gear, died in 1947. It depicts Christ offering a benediction of peace, with his head and hands raised skyward; the statue was subsequently dedicated to the memory of Marcante.

Due to increasing amounts of corrosion and the growth of crustaceans, the statue was removed from the water and restored in 2003. A hand, detached by an anchor, was replaced; the statue was returned to the water with a new base on 17 July 2004. The statue was cleaned in 2018. A second bronze sculpture, cast from the same mold as the original bronze statue, exists off the coast of St. George's, Grenada, it was a gift of the navy of Genoa for assistance in rescuing the crew of the Italian vessel MV Bianca C., destroyed by fire in the port of St. George's; the sculpture was placed underwater on October 22, 1961. A third bronze statue, from the original mold, was presented to the Underwater Society of America in New York in 1962, shipped by boat to Chicago, where it was set up for unveiling in the ballroom of the Palmer House Hotel at the Underwater Society of America 1962 convention. On August 25, 1965, it was placed in 25 feet of water off the coast of Key Largo, near Dry Rocks six miles east of Key Largo in the National Marine Sanctuary, just outside of John Pennekamp State Park.

The statue weighs around 260 kg, the concrete base to which it is attached weighs 9 tons. In Part 3 of the Netflix Original series Bloodline, Danny Rayburn is seen taking guests at his family's Monroe County, Florida inn, Rayburn House, snorkeling at Christ of the Abyss in Florida. An image of one of the statues was used as cover art, both for BT's Ima, for God Lives Underwater's debut album Empty. "Christ of the Abyss". Dive Spots. Archived from the original on 17 October 2017. "LIFE Magazine article".. Sculpture Christ of the Deep

Escape of the Living Dead

Escape of the Living Dead is a five-issue zombie comic book miniseries published by Avatar Press, published in 2005. It is written by John A. Russo with artwork by Dheeraj Verma. Although the story is a sequel to Night of the Living Dead, it is not set in the continuity of George Romero’s series of films or Russo’s The Return of the Living Dead series, it was followed in 2006 by Escape of the Living Dead Fearbook and Escape of the Living Dead: Airborne, a three-issue miniseries, Escape of the Living Dead Annual, published in 2007. Set in 1971, 3 years after the events seen in Night of the Living Dead, the comic starts out with a raid by police officers led by Sheriff Harkness on a medical lab run by Dr. Melrose. During the raid the officers manage to shoot Dr. Melrose. Before he dies he reveals he had been experimenting on the zombies for a government funded project and tells the officers about his son, taking over the project. Meanwhile, one of the main characters, Sally Brinkman, is talking to her father Henry.

It is revealed Sally is staying with her parents whilst going through a divorce and is working for her father at the local saloon. Two robbers for the gang Sons of Satan attempt to rob a truck by pouring sugar in the gas tank, robbing its contents; when they look in the truck, they find it is full of zombies that proceed to eat them. With the zombies released they start walking towards the town; the zombies reach the Brinkman farm and kill Sally’s mother. The zombies try to attack Sally, but she manages to avoid them and ride a horse to the saloon where her Dad works. However, zombies have attacked the saloon as well, they both lock the doors. Meanwhile, the rest of the Sons of Satan gang attempt to meet up with the robbers from before, only to encounter them now as zombies; the three gang members, Bearcat and Honeybear, kill the zombies before driving off. They reach the saloon, where they are surrounded by zombies. Sally and Henry let them in; the zombies start to break in, the bikers attempt to escape, kidnapping Sally and stealing a truck in the process, leaving Henry to be eaten.

During this, one of the bikers, Honeybear, is killed, while Henry manages to avoid the zombies and get a truck to chase after the bikers. Meanwhile, the two bikers and Sally have taken refuge in the nearby woods. Sally is now tied up. Although they fight off the zombies, Slam is bitten and, in panic, kills Bearcat, he forces Sally to take him to her house to help him. At this time, Sheriff Harkness discovers the truck that the zombies were transported in. At this point Henry shows up, helps Sheriff Harkness decide to get a posse together to kill the zombies. Back at Sally’s farm, Sally is forced to help Slam clean his wounds. Slam tries to kill her, but is killed by a hidden zombie. Sally runs outside to find her father and a posse killing the zombies; the posse fight a horde of zombies, which attack them. Although outnumbered, the military kill all the zombies. After the fight Sheriff Harkness gets a call on the radio, saying that the Dr. Melrose that they killed at the beginning did not match the dental records, thus was an impostor.

The last pages shows a lone zombie being captured by the real Dr. Melrose and his son, implying the zombie epidemic is far from over. Escape of the Living Dead #1 was published with 13 different cover art versions. Dheeraj Verma created seven - "Regular", American Badass, "Blood Red Con Foil", "Gold Foil", "Gore", "Red Foil Russo Signed" and "Wraparound" versions. Escape of the Living Dead #2 was published with 9 different cover art versions. Dheeraj Verma created six - "Regular", "Ghostly", "Gold Foil", "Gore", "Topless" and "Wraparound". Escape of the Living Dead #3 was published with 7 different cover art versions. Dheeraj Verma created five - "Regular", "Captive", "Gore", "Trapped", "Wraparound". Escape of the Living Dead #4 was published with 7 different cover art versions. Dheeraj Verma created five - "Regular", "Gore", "Terror" and "Wraparound". Escape of the Living Dead #5 was published with 8 different cover art versions. Dheeraj Verma created five - "Regular", "Gore", "Terror", "Wraparound".

The series has been collected into two trade paperbacks: Escape of the Living Dead Escape of the Living Dead: Resurrected A film adaptation - to be directed by John Russo and starring Tony Todd, Kane Hodder, Amber Stevens, Kristina Klebe and Gunnar Hansen - was announced in 2008. However, this version never came to fruition; as of 2015, Russo is still trying to develop the film project. List of zombie novels Escape of the Living Dead at Avatar Press

Jan Baars

Joannes Antonius Baars was a leading Dutch fascist during the 1930s. During the 1920s Baars emerged as part of the group associated with De Bezem, a fascist journal aimed at the poor; the magazine split in 1930 and Baars supported Alfred Haighton over H. A. Sinclair de Rochemont, joining Haighton's Fascistische Jongeren Bond; the two quarrelled in 1932 however and the rabble-rousing Baars soon set up his own movement, the General Dutch Fascist League. The stated purpose of this new group was to unite the various strands of fascism within the Netherlands under a single umbrella. Baars gained some support amongst the poor as his coarse, down-to-earth style of rhetoric could be identified with by people who spoke in the same manner; this group joined Haighton's movement and the National Union in 1933 to form a'corporative concentration', although Baars, a market trader by profession, had little time for Carel Gerretson, the university professor who led the new group. He that group soon fell apart.

After a brief involvement in opposing Anton Mussert and the NSB, Baars quit politics in 1936 and returned to market trading. Having criticized Adolf Hitler's treatment of the Jews, Baars played no role in collaboration and was active in the Dutch resistance

David Attie

David Attie was a prominent American commercial and fine art photographer, published in magazines and books from the late 1950s until his passing in the 1980s, was one of the last great proteges of influential photography teacher and art director Alexey Brodovitch. Attie worked in a wide range of styles, creating the best-known portraits of playwright Lorraine Hansberry and illustrating everything from novels to album covers to the work of Truman Capote, but he was best known in his lifetime for multiple imagery—highly inventive, pre-Photoshop montages made by combining negatives in the darkroom—and for a style of portraiture in which the subjects themselves controlled the exposure. His work has received newfound attention with the 2015 publication of his Capote collaboration "Brooklyn: A Personal Memoir, With The Lost Photographs of David Attie," a 2016-18 exhibit of his early work at the Brooklyn Historical Society, the inclusion of his work in many recent publications and documentaries.

Attie grew up in Bensonhurst and graduated from Erasmus Hall High School, the same alma mater as Bobby Fischer, whom Attie photographed. He attended the Kansas City Art Institute and Cooper Union. During his Army service, Attie painted pinup-style portraits on the noses of combat planes. Attie worked as a commercial illustrator under the name Dave Attie. Attie began his photographic career as a student and protege of famed Harper's Bazaar art director Alexey Brodovitch, who had mentored the careers of Richard Avedon, Irving Penn, Diane Arbus, Attie's close friend Hiro; when Attie studied under Brodovitch, his legendary "Design Laboratory" course at The New School For Social Research -- which Brodovitch used to discover new talent for Bazaar -- was held in Avedon's photo studio. As Attie's son has written, his success in Brodovitch's famously difficult course was the result of a creative accident: "One night, was developing film for his first class assignment, when he realized he’d underexposed every single frame.

Class was the next day. In other words, he was toast --. In a desperate panic, he started layering the negatives together, to create moody, impressionistic photo montages, his life must have been flashing before his eyes, at the wrong exposure. Brodovitch loved the montages, he spent the entire class gushing over them."On the final night of the course, Brodovitch gave Attie his first professional assignment, to create a series of photo montages to illustrate Truman Capote's newest work, Breakfast at Tiffany's, for Bazaar in 1958. But while Attie completed the montages, Capote began to clash with the publisher of Bazaar, the Hearst Corporation, over the tart language and subject matter of his novella. Alice Morris, the magazine's literary editor recounted that Capote agreed to make the changes Hearst wanted "partly because I showed him the layouts... six pages with beautiful, atmospheric photographs." But in the end, Hearst decided. When Capote resold the novella to Esquire, he specified that he "would not be interested if did not use Attie's photographs."

He wrote to Esquire fiction editor Rust Hills, "I'm happy that you are using his pictures, as I think they are excellent." But to Capote's disappointment, Esquire used just one full-page image of Attie's. Attie's work on the project nonetheless launched his career, gaining him further assignments from both Bazaar and Brodovitch. Attie went on to shoot portraits of Capote and to illustrate his essay Brooklyn Heights: A Personal Memoir for Holiday Magazine; some of Attie's unused Breakfast at Tiffany's montages were modified and used to illustrate Bill Manville's 1960 memoir Saloon Society, The Diary of a Year Beyond Aspirin, designed by Brodovitch. Brodovitch biographer Kerry William Purcell has described Attie's work on this book as "an inspired set of experimental images."From that point forward, Attie’s commercial work was prolific and wide-ranging – including frequent covers and spreads for Vogue, Newsweek and Bazaar. Attie collaborated again with Brodovitch on a still-renowned special section of Harper's than ran in October 1959, "Writing in America,", edited by future New York Review of Books editor Robert B. Silvers and used Attie’s images to illustrate essays by Budd Schulberg, Kingsley Amis, Archibald MacLeish and others.

Attie did the photos for a 1964 pinup book of Jayne Mansfield cal

Gmina Skrwilno

Gmina Skrwilno is a rural gmina in Rypin County, Kuyavian-Pomeranian Voivodeship, in north-central Poland. Its seat is the village of Skrwilno, which lies 12 kilometres south-east of Rypin and 66 km east of Toruń; the gmina covers an area of 124.35 square kilometres, as of 2006 its total population is 6,109. Gmina Skrwilno contains the villages and settlements of Baba, Budziska, Czarnia Duża, Czarnia Mała, Kotowy, Mościska, Nowe Skudzawy, Otocznia, Rak, Skrwilno, Szczawno, Szustek, Urszulewo, Wólka and Zofiewo. Gmina Skrwilno is bordered by the gminas of Lubowidz, Rogowo, Rościszewo, Rypin, Świedziebnia and Szczutowo. Polish official population figures 2006