Kyoto Journal of Mathematics

Bayer–Macrì decomposition on Bridgeland moduli spaces over surfaces

Wanmin Liu

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We find a decomposition formula of the local Bayer–Macrì map for the nef line bundle theory on the Bridgeland moduli space over a surface. If there is a global Bayer–Macrì map, then such a decomposition gives a precise correspondence from Bridgeland walls to Mori walls. As an application, we compute the nef cone of the Hilbert scheme S[n] of n-points over special kinds of a fibered surface S of Picard rank 2.

Article information

Kyoto J. Math., Volume 58, Number 3 (2018), 595-621.

Received: 1 November 2016
Revised: 29 November 2016
Accepted: 29 November 2016
First available in Project Euclid: 20 June 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}
Secondary: 18E30: Derived categories, triangulated categories 14E30: Minimal model program (Mori theory, extremal rays)

Bayer–Macrì map Bridgeland stability condition minimal model program moduli space of complexes wall crossing


Liu, Wanmin. Bayer–Macrì decomposition on Bridgeland moduli spaces over surfaces. Kyoto J. Math. 58 (2018), no. 3, 595--621. doi:10.1215/21562261-2017-0031.

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