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Olivier Penacchio. (2011). Mixed Hodge Structures and Equivariant Sheaves on the Projective Plane. MN - Mathematische Nachrichten, 284(4), 526–542.
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
Keywords: Mixed Hodge structures, equivariant sheaves, MSC (2010) Primary: 14C30, Secondary: 14F05, 14M25
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