Nef divisors for moduli spaces of complexes with compact support
arXiv:1602.00863
Abstract
In [BM14b], the first author and Macrì constructed a family of nef divisors on any moduli space of Bridgeland-stable objects on a smooth projective variety X. In this article, we extend this construction to the setting of any separated scheme Y of finite type over a field, where we consider moduli spaces of Bridgeland-stable objects on Y with compact support. We also show that the nef divisor is compatible with the polarising ample line bundle coming from the GIT construction of the moduli space in the special case when Y admits a tilting bundle and the stability condition arises from a θ-stability condition for the endomorphism algebra. Our main tool generalises the work of Abramovich--Polishchuk [AP06] and Polishchuk [Pol07]: given a t-structure on the derived category D_c(Y) on Y of objects with compact support and a base scheme S, we construct a constant family of t-structures on a category of objects on YxS with compact support relative to S.
36 pages. In memory of Johan Louis Dupont. V2: updated following comments from the referee and from Joe Karmazyn who gave a counterexample to a false claim in version 1. To appear in Selecta Math
References in corpus (5)
- Birational models of moduli spaces of coherent sheaves on the projective plane
- Projectivity and Birational Geometry of Bridgeland Moduli spaces on an Enriques Surface
- Extremal rays and automorphisms of holomorphic symplectic varieties
- Dimer models and crepant resolutions
- Quiver GIT for Varieties with Tilting Bundles