Moduli spaces of stable sheaves on abelian surfaces

By K. Yoshioka. 2000

355 citations recorded by the source corpus.

Abstract. In this paper, we consider basic problems on moduli spaces of stable sheaves on abelian surfaces. Our main assumption is the primitivity of the associated Mukai vector. We determine the deformation types, albanese maps, Bogomolov factors and their weight 2 Hodge structures. We also discuss the deformation types of moduli spaces of stable sheaves on K3 surfaces.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f1dd5c21cb11f52bd0ea883c48780c73a0ad0794

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Citations in the corpus

Deformation of the O'Grady moduli spaces (2010, background): “is commutative, and this is shown to be true by standard computations (see for example [24], Proposition 2.”
The integral Hodge conjecture for two-dimensional Calabi–Yau categories (2020, background): “15] (based on [94, 95]), and for T an abelian surface and α = 0 this is [8, Theorem”
Prime exceptional divisors on holomorphic symplectic varieties and monodromy reflections (2009, background): “ducible holomorphic symplectic variety of K3[n] type, with n= (v,v)+2 2 . This result is due to several people, including Huybrechts, Mukai, O’Grady, and Yoshioka. It can be found in its ﬁnal form in [Y2]. Over S×MH(v) there exists a universal sheaf F, possibly twisted with respect to a non-trivial ”
Lagrangian Fibrations of Holomorphic-Symplectic Varieties of K3[n]-Type (2013, background): “[n]-type, with n= (v,v)+2 2 = d2(ξ,ξ)+2 2 . This is a special case of a result, which is due to several people, including Huybrechts, Mukai, O’Grady, and Yoshioka. It can be found in its ﬁnal form in [Y1]. Over S× MH(v) there exists a universal sheaf F, possibly twisted with respect to a non-trivial”
Hitchin fibrations, abelian surfaces, and the P=W conjecture (2019, neutral): “Firstly, since the Mukai vectors (49) vβ and vβ′ are primitive with the same Mukai length, v2β = v 2 β′ ∈ Z, we can apply [41, Theorem 8.3] (which follows from Yoshioka [51]) to find isometries g1 : H ∗(A,Z) → H∗(A′,Z), φ1 : H ∗(Mβ,A,Q) → H ∗(Mβ′,A′ ,Q) such that g1(vβ) = vβ′ and (62) (g1 ⊗ φ1)ch(Fβ”
INTEGRAL CONSTRAINTS ON THE MONODROMY GROUP OF THE HYPERKÄHLER RESOLUTION OF A SYMMETRIC PRODUCT OF A K3 SURFACE (2006, background): “ not need the intrinsic formula, but only the fact that it is monodromy invariant and its identiﬁcation in the following theorem due to Mukai, Huybrechts, O’Grady, and Yoshioka: 12 Theorem 2.3 ([OG], [Y2] Theorem 8.1, and [Y3] Corollary 3.15) Let vbe a primitive and eﬀective class and Ha v-generic a”
Automorphism groups of Calabi-Yau manifolds of Picard number two (2012, background): “X) is the Picard number of X. There are many interesting Calabi-Yau manifolds of Picard number 2 (for instance, [PSS71], [We88], [GP01], [Ku03], [Ku04] [Ca07], [Sc11], [OS01], [HT01], [HT09], [HT09], [Yo01], [Yo12], [Ogr05], [Sa07]). We denote by (xn) X, where dim X = n, the top interesection form o”
Monodromy and birational geometry of O'Grady's sixfolds (2019, methodology): “In this subsection we recall, and adapt to our context where necessary, two results on isomorphisms between moduli spaces exhibited by Yoshioka in §3 of [42].”