𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Graded rings and equivariant sheaves on toric varieties

✍ Scribed by Markus Perling

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
258 KB
Volume
263-264
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

In this note we derive a formalism for describing equivariant sheaves over toric varieties. This formalism is a generalization of a correspondence due to Klyachko, which states that equivariant vector bundles on toric varieties are equivalent to certain sets of filtrations of vector spaces. We systematically construct the theory from the point of view of graded ring theory and this way we clarify earlier constructions of Kaneyama and Klyachko. We also connect the formalism to the theory of fine‐graded modules over Cox' homogeneous coordinate ring of a toric variety. As an application we construct minimal resolutions of equivariant vector bundles of rank two on toric surfaces. (Β© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

πŸ“œ SIMILAR VOLUMES

Cohomology on Toric Varieties and Local
Cohomology on Toric Varieties and Local Cohomology with Monomial Supports
✍ David Eisenbud; Mircea MustaΕ£a; Mike Stillman πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 295 KB

In this note we describe aspects of the cohomology of coherent sheaves on a complete toric variety X over a field k and, more generally, the local cohomology, with supports in a monomial ideal, of a finitely generated module over a polynomial ring S. This leads to an efficient way of computing such

Moduli for equivariant vector bundles of
Moduli for equivariant vector bundles of rank two on smooth toric surfaces
✍ Markus Perling πŸ“‚ Article πŸ“… 2004 πŸ› John Wiley and Sons 🌐 English βš– 197 KB πŸ‘ 1 views

## Abstract We give a complete classification of equivariant vector bundles of rank two over smooth complete toric surfaces and construct moduli spaces of such bundles. This note is a direct continuation of an earlier note where we developed a general description of equivariant sheaves on toric var