We study a class of semihomogeneous vector bundles over the product of an abelian variety and its dual. For abelian surfaces, we connect these semihomogeneous bundles to the Verlinde bundles of generalized theta functions constructed from the moduli spaces of sheaves.

Let X be a compact Calabi–Yau 3-fold, and write M , ? for the moduli stacks of objects in coh ( ) D b . There are natural line bundles K ? analogues canonical bundles. Orientation data on is an isomorphism class square root 1 / 2 satisfying compatibility condition stack short exact sequences. It was introduced by Kontsevich Soibelman [35, §5] their theory motivic Donaldson–Thomas invariants, al...

Suppose X is a locally noetherian Deligne–Mumford stack. Definition 1.2 has an obvious variant X̂ét using the underlying smaller étale site Xét and the restriction Oc Xét of Oc X to this site. By [3, 12.7.4], the category of cartesian Oc X -modules on Xlis-ét is equivalent to the category of Oc Xét-modules on Xét: (1.1) ModXlis-ét,cart(Oc X ) ' ModXét(Oc Xét) Definition 1.3. Let X be a locally n...

In each dimension n ≥ 3 there are many projective simplicial toric varieties whose Grothendieck groups of vector bundles are at least as big as the ground field. In particular, the conjecture that the Grothendieck groups of locally trivial sheaves and coherent sheaves on such varieties are rationally isomorphic fails badly.

We interprete results of Markman on monodromy operators as a universality statement for descendent integrals over moduli spaces stable sheaves K3 surfaces. This yields effective methods to reduce these the punctual Hilbert scheme surface. As an application we establish higher rank Segre-Verlinde correspondence surfaces conjectured by Göttsche and Kool.

We study birational morphisms between smooth projective surfaces that respect a given Poisson structure, with particular attention to induced birational maps between the (Poisson) moduli spaces of sheaves on those surfaces. In particular, to any birational morphism, we associate a corresponding “minimal lift” operation on sheaves of homological dimension ≤ 1, and study its properties. In partic...

In this paper, we shall consider the birational structure of moduli of stable sheaves on elliptic surfaces, which is a generalization of Friedman’s results to higher rank cases. As applications, we show that some moduli spaces of stable sheaves on P 2 are rational. We also compute the Picard groups of those on Abelian surfaces.