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Mixed Hodge structures and equivariant sheaves on the projective plane

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Abstract

We describe an equivalence of categories between the category of mixed Hodge structures and a category of equivariant vector bundles on a toric model of the complex projective plane which verify some semistability condition. We then apply this correspondence to define an invariant which generalizes the notion of R-split mixed Hodge structure and give calculations for the first group of cohomology of possibly non smooth or non-complete curves of genus 0 and 1. Finally, we describe some extension groups of mixed Hodge structures in terms of equivariant extensions of coherent sheaves.
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Original languageEnglish
Pages (from-to) 526-542
Number of pages17
JournalMathematische Nachrichten
Volume284
Issue number4
DOIs
Publication statusPublished - Mar 2011

    Research areas

  • Algebraic geometry , Hodge theory, Mixed Hodge structures, Equivariant sheaves, Toric varieties

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