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The Effective Cone of Moduli Spaces of Sheaves on a Smooth Quadric Surface

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posted on 19.10.2016 by Timothy L. Ryan
In this paper, we provide an approach to computing the effective cone of moduli spaces of sheaves on a smooth quadric surface. We find Brill-Noether divisors spanning extremal rays of the effective cone using resolutions of the general elements of the moduli space which are found using the machinery of exceptional bundles. We use this approach to provide many examples of extremal rays in these effective cones. In particular, we completely compute the effective cone of the first fifteen Hilbert schemes of points on a smooth quadric surface.

History

Advisor

Coskun, Izzet

Department

Mathematics, Statistics, and Computer Science

Degree Grantor

University of Illinois at Chicago

Degree Level

Doctoral

Committee Member

Ein, Lawrence Huizenga, Jack Riedl, Eric Tucker, Kevin

Submitted date

2016-08

Language

en

Issue date

19/10/2016

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