Flops on holomorphic symplectic fourfolds and determinantal cubic hypersurfaces
نویسندگان
چکیده
منابع مشابه
Rational curves on holomorphic symplectic fourfolds
One main problem in the theory of irreducible holomorphic symplectic manifolds is the description of the ample cone in the Picard group. The goal of this paper is to formulate explicit Hodge-theoretic criteria for the ampleness of line bundles on certain irreducible holomorphic symplectic manifolds. It is well known that for K3 surfaces the ample cone is governed by (−2)-curves. More generally,...
متن کاملFoliations on hypersurfaces in holomorphic symplectic manifolds
Let Y be a hypersurface in a 2n-dimensional holomorphic symplectic manifold X. The restriction σ|Y of the holomorphic symplectic form induces a rank one foliation on Y . We investigate situations where this foliation has compact leaves; in such cases we obtain a space of leaves Y/F which has dimension 2n − 2 and admits a holomorphic symplectic form.
متن کاملTwisted Fourier-Mukai transforms for holomorphic symplectic fourfolds
We apply the methods of Căldăraru to construct a twisted FourierMukai transform between a pair of holomorphic symplectic four-folds. More precisely, we obtain an equivalence between the derived category of coherent sheaves on a certain four-fold and the derived category of twisted sheaves on its ‘mirror’ partner. As corollaries, we show that the two spaces are connected by a one-parameter famil...
متن کاملTwisted Cubics on Cubic Fourfolds
We construct a new twenty-dimensional family of projective eight-dimensional holomorphically symplectic manifolds: the compactified moduli space M3(Y ) of twisted cubics on a smooth cubic fourfold Y that does not contain a plane is shown to be smooth and to admit a contraction M3(Y ) → Z(Y ) to a projective eight-dimensional symplectic manifold Z(Y ). The construction is based on results on lin...
متن کاملOn symplectic hypersurfaces
A symplectic variety is a normal complex variety X with a holomorphic symplectic form ω on the regular part X reg and with rational Gorenstein sin-gularities. Affine symplectic varieties arise in many different ways such as closures of nilpotent orbits of a complex simple Lie algebra, as Slodowy slices to such nilpotent orbits or as symplectic reductions of holomorphic symplec-tic manifolds wit...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Institute of Mathematics of Jussieu
سال: 2009
ISSN: 1474-7480,1475-3030
DOI: 10.1017/s1474748009000140