Mixed Hodge structures and equivariant sheaves on the projective plane |
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Authors: | Olivier Penacchio |
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Affiliation: | CRM, Apartat 50, E‐08193 Bellaterra, Spain |
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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. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim |
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Keywords: | Mixed Hodge structures equivariant sheaves MSC (2010) Primary: 14C30 Secondary: 14F05 14M25 |
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