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Graded rings and equivariant sheaves on toric varieties
Author(s) -
Perling Markus
Publication year - 2004
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310130
Subject(s) - equivariant map , mathematics , vector bundle , formalism (music) , pure mathematics , toric variety , homogeneous , derived category , algebra over a field , combinatorics , functor , art , musical , visual arts
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. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)