Nef divisors for moduli spaces of complexes with compact support
- First Online:
- Cite this article as:
- Bayer, A., Craw, A. & Zhang, Z. Sel. Math. New Ser. (2017) 23: 1507. doi:10.1007/s00029-016-0298-y
In Bayer and Macrì (J Am Math Soc 27(3):707–752, 2014), 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 \(\theta \)-stability condition for the endomorphism algebra. Our main tool generalises the work of Abramovich–Polishchuk (J Reine Angew Math 590:89–130, 2006) and Polishchuk (Mosc Math J 7(1):109–134, 2007): 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 \(Y \times S\) with compact support relative to S.
KeywordsBridgeland stability conditions Derived categories t-structures Moduli spaces of sheaves and complexes Nef divisors
Mathematics Subject ClassificationPrimary 14D20 Secondary 14F05 14J28 18E30
|Funder Name||Grant Number||Funding Note|
|University of Bath|
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.