A global Torelli theorem for rigid hyperholomorphic sheaves

2013/10/22 by Markman, Eyal, Mehrotra, Sukhendu
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1310.5782

Abstract

We prove a global Torelli theorem for the moduli space of marked triples (X,m,A), consisting of an irreducible holomorphic symplectic manifold X, a marking m of its second integral cohomology, and a stable and rigid sheaf A of Azumaya algebras on the cartesian product X^d, d>0, such that the second Chern class of A is invariant under a finite index subgroup of the monodromy group of X. The main example involves the rank 2n-2 sheaf over the cartesian square of holomorphic symplectic manifolds of K3[n]-type considered in the work of the first author arXiv:1105.3223. The result will be used in the authors forthcoming work on generalized deformations of K3 surfaces.

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