A combinatorial description of stability for toric vector bundles
Lucie Devey (IF)
TL;DR
This paper provides a combinatorial framework to characterize the stability of toric vector bundles using polytopes, extending previous geometric descriptions and linking subbundles to subparliaments.
Contribution
It introduces a novel combinatorial approach to stability for toric vector bundles via parliaments of polytopes, generalizing moment polytope concepts.
Findings
Characterization of stability through parliaments of polytopes
Definition of subparliaments corresponding to subbundles
Extension of moment polytope theory for toric vector bundles
Abstract
The aim of this paper is to discuss a combinatorial characterisation of stability for toric vector bundles (or equivariant reflexive sheaves) in the terms of their parliaments of polytopes, a generalization of moment polytopes for toric vector bundles by Di Rocco, Jabbusch and Smith. We also define subparliaments of polytopes and identify them with parliaments of equivariant subbundles.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry · Algebraic Geometry and Number Theory