%0 Journal Article
%T Mixed Hodge Structures and Equivariant Sheaves on the Projective Plane
%A Olivier Penacchio
%E R. Mennicken
%J Mathematische Nachrichten
%D 2011
%V 284
%N 4
%I WILEY-VCH Verlag
%@ 1522-2616
%F Olivier Penacchio2011
%O CIC
%O exported from refbase (http://refbase.cvc.uab.es/show.php?record=1721), last updated on Thu, 10 May 2012 11:46:51 +0200
%X 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
%K Mixed Hodge structures
%K equivariant sheaves
%K MSC (2010) Primary: 14C30
%K Secondary: 14F05
%K 14M25
%U http://onlinelibrary.wiley.com/doi/10.1002/mana.200710219/full
%U http://refbase.cvc.uab.es/files/Pen2011.pdf
%U http://dx.doi.org/10.1002/mana.200710219
%P 526-542