TY  - JOUR
AU  - Olivier Penacchio
ED  - R. Mennicken
PY  - 2011//
TI  - Mixed Hodge Structures and Equivariant Sheaves on the Projective Plane
T2  - MN
JO  - Mathematische Nachrichten
SP  - 526
EP  - 542
VL  - 284
IS  - 4
PB  - WILEY-VCH Verlag
KW  - Mixed Hodge structures
KW  - equivariant sheaves
KW  - MSC (2010) Primary: 14C30
KW  - Secondary: 14F05
KW  - 14M25
N2  - 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
SN  - 1522-2616
UR  - http://onlinelibrary.wiley.com/doi/10.1002/mana.200710219/full
L1  - http://refbase.cvc.uab.es/files/Pen2011.pdf
UR  - http://dx.doi.org/10.1002/mana.200710219
N1  - CIC
ID  - Olivier Penacchio2011
ER  -