Moduli of toric vector bundles

Details Moduli of toric vector bundles Moduli of toric vector bundles

2007-05-03

arxiv.org/abs/0705.0410v2

Compositio Math. 144 (2008), 1199--1213.

Mathematics

Algebraic Geometry

16 pages. v2: corrected inconsistencies in sign conventions, other minor changes. To appear in Compos. Math

Scientific paper

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.

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