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Moduli of toric vector bundles

Part of: (Co)homology theory Families, fibrations Surfaces and higher-dimensional varieties Special varieties

Published online by Cambridge University Press:  01 September 2008

Sam Payne
Sam Payne*
Affiliation:
Stanford University, Mathematics, Building 380, Stanford, CA 94305, USA (email: spayne@stanford.edu)
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Abstract

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We give a presentation of the moduli stack of toric vector bundles with fixed equivariant total Chern class as a quotient of a fine moduli scheme of framed bundles by a linear group action. This fine moduli scheme is described explicitly as a locally closed subscheme of a product of partial flag varieties cut out by combinatorially specified rank conditions. We use this description to show that the moduli of rank three toric vector bundles satisfy Murphy’s law, in the sense of Vakil. The preliminary sections of the paper give a self-contained introduction to Klyachko’s classification of toric vector bundles.

Keywords

toric varietiesvector bundlesmoduli spaces

MSC classification

Secondary: 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli 14D20: Algebraic moduli problems, moduli of vector bundles 14F05: Sheaves, derived categories of sheaves and related constructions 14J10: Families, moduli, classification 14M25: Toric varieties, Newton polyhedra
Type
Research Article
Information
Compositio Mathematica , Volume 144 , Issue 5 , September 2008 , pp. 1199 - 1213
Copyright
Copyright © Foundation Compositio Mathematica 2008