Reference : On 1-dimensional sheaves on projective plane
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On 1-dimensional sheaves on projective plane
Iena, Oleksandr mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Workshop - Higgs bundles and Hitchin system - VBAC2016
from 11-01-2016 to 15-01-2016
[en] Simpson moduli spaces ; coherent sheaves ; vector bundles on curves ; singular sheaves
[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.
Researchers ; Professionals

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