Selecta Mathematica

, Volume 23, Issue 2, pp 1507–1561

Nef divisors for moduli spaces of complexes with compact support

Open Access

DOI: 10.1007/s00029-016-0298-y

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.


Bridgeland stability conditions Derived categories t-structures Moduli spaces of sheaves and complexes Nef divisors 

Mathematics Subject Classification

Primary 14D20 Secondary 14F05 14J28 18E30 

Funding information

Funder NameGrant NumberFunding Note
University of Bath

    Copyright information

    © The Author(s) 2016

    Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, 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.

    Authors and Affiliations

    1. 1.School of Mathematics and Maxwell InstituteThe University of EdinburghEdinburghScotland, UK
    2. 2.Department of Mathematical SciencesUniversity of BathClaverton Down, BathUK
    3. 3.Institute for Algebraic GeometryLeibniz University HannoverHannoverGermany

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