Moduli spaces of torsion sheaves on K3 surfaces and derived equivalences
نویسندگان
چکیده
منابع مشابه
Equivalences of Derived Categories and K3 Surfaces
We consider derived categories of coherent sheaves on smooth projective varieties. We prove that any equivalence between them can be represented by an object on the product. Using this, we give a necessary and sufficient condition for equivalence of derived categories of two K3 surfaces.
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Matsuki and Wentworth [M-W] constructed the moduli space of w-twisted semi-stable sheaves E with v(E) = v. We denote it by M w H(v). If w = v(OX), then the v(OX)-twisted semi-stability is nothing but the usual Gieseker’s semi-stability. Hence we denote M v(OX) H (v) by MH(v). Assume that v is an isotropic Mukai vector. In [A], Abe considered the singularities of MH(v). Replacing MH(v) by M v H(...
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Matsuki and Wentworth [M-W] constructed the moduli space of w-twisted semi-stable sheaves E with v(E) = v. We denote it by M w H(v). If w = v(OX), then v(OX)-twisted semi-stability is nothing but the usual Gieseker’s semi-stability. Hence we denote M v(OX) H (v) by MH(v). Assume that v is an isotropic Mukai vector. In [A], Abe considered the singularities of MH(v). Replacing MH(v) by M v H(v), ...
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A compact Kähler surface X is a K3 surface if it is simply connected and it carries a global homolorphic symplectic form (i.e. the canonical bundle KX ∼= OX). An example is given by the Fermat quartic: consider the degree four polynomial P (X0, ..., X3) = X 4 0 + X 4 1 + X 4 2 + X 4 3 ∈ C[X0, ..., X3]. The vanishing locus S = V (P ) is an irreducible quartic hypersurface in PC, which is simply ...
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LetX be an algebraicK3 surface. Fix an ample divisorH onX ,L ∈ Pic(X) and c2 ∈ Z. Let MH(r;L, c2) be the moduli space of rank r, H-stable vector bundles E over X with det(E) = L and c2(E) = c2. The goal of this paper is to determine invariants (r; c1, c2) for which MH(r;L, c2) is birational to some Hilbert scheme Hilb(X).
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2016
ISSN: 0024-6107,1469-7750
DOI: 10.1112/jlms/jdw022