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On 1-dimensional sheaves on projective plane
Iena, Oleksandr
2016
 

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Keywords :
Simpson moduli spaces; coherent sheaves; vector bundles on curves; singular sheaves
Abstract :
[en] Let M be the Simpson moduli space of semistable sheaves on the projective plane with fixed linear Hilbert polynomial P(m)=dm+c. A generic sheaf in M is a vector bundle on its Fitting support, which is a planar projective curve of degree d. The sheaves that are not vector bundles on their support constitute a closed subvariety M' in M. We study the geometry of M' in the case of Hilbert polynomials dm-1 (for d bigger than 3) and demonstrate that M' is a singular variety of codimension 2 in M. We speculate on how the question we study is related to recompactifying of the Simpson moduli spaces by vector bundles.
Disciplines :
Mathematics
Author, co-author :
Iena, Oleksandr ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Language :
English
Title :
On 1-dimensional sheaves on projective plane
Publication date :
January 2016
Event name :
Workshop - Higgs bundles and Hitchin system - VBAC2016
Event place :
Lausanne, Switzerland
Event date :
from 11-01-2016 to 15-01-2016
Audience :
International
Available on ORBilu :
since 18 January 2016

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