A very general sextic double solid is not stably rational
نویسندگان
چکیده
منابع مشابه
Hypersurfaces that are not stably rational
A fundamental problem of algebraic geometry is to determine which varieties are rational, that is, isomorphic to projective space after removing lower-dimensional subvarieties from both sides. In particular, we want to know which smooth hypersurfaces in projective space are rational. An easy case is that smooth complex hypersurfaces of degree at least n + 2 in P are not covered by rational curv...
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I t is well known that a Cremona transformation T with ten or fewer jF-points will transform a rational sextic S into a rational sextic S' when the F-points of T are all located at the nodes of S. I have shown (cf. [ l ] , p. 248, (9); [2], p. 255, (5)) that, even though the number of transformations T of the type indicated is infinite, the transforms S' are all included in 2 • 31 -51 classes, ...
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Motivated by the Beauville–Voisin conjecture about Chow rings of powers of K3 surfaces, we consider a similar conjecture for Chow rings of powers of EPW sextics. We prove part of this conjecture for the very special EPW sextic studied by Donten–Bury et alii. We also prove some other results concerning the Chow groups of this very special EPW sextic, and of certain related hyperkähler fourfolds....
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2016
ISSN: 0024-6093,1469-2120
DOI: 10.1112/blms/bdv098