PT Journal
AU Olivier Penacchio
TI Mixed Hodge Structures and Equivariant Sheaves on the Projective Plane
SO Mathematische Nachrichten
JI MN
PY 2011
BP 526
EP 542
VL 284
IS 4
DI 10.1002/mana.200710219
DE Mixed Hodge structures; equivariant sheaves; MSC (2010) Primary: 14C30; Secondary: 14F05; 14M25
AB 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
ER