@Article{OlivierPenacchio2011,
author="Olivier Penacchio",
editor="R. Mennicken",
title="Mixed Hodge Structures and Equivariant Sheaves on the Projective Plane",
journal="Mathematische Nachrichten",
year="2011",
publisher="WILEY-VCH Verlag",
volume="284",
number="4",
pages="526--542",
optkeywords="Mixed Hodge structures",
optkeywords="equivariant sheaves",
optkeywords="MSC (2010) Primary: 14C30",
optkeywords="Secondary: 14F05",
optkeywords="14M25",
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. {\textcopyright} 2011 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim",
optnote="CIC",
optnote="exported from refbase (http://refbase.cvc.uab.es/show.php?record=1721), last updated on Thu, 10 May 2012 11:46:51 +0200",
issn="1522-2616",
doi="10.1002/mana.200710219",
opturl="http://onlinelibrary.wiley.com/doi/10.1002/mana.200710219/full",
file=":http://refbase.cvc.uab.es/files/Pen2011.pdf:PDF"
}