[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
