Universal plane curve and moduli spaces of 1-dimensional coherent sheaves
Algebraic Geometry
2014-01-09 v3
Abstract
We show that the universal plane curve M of fixed degree d > 2 can be seen as a closed subvariety in a certain Simpson moduli space of 1-dimensional sheaves on a projective plane contained in the stable locus. The universal singular locus coincides with the subvariety of M consisting of sheaves that are not locally free on their support. It turns out that the blow up of M along M' may be naturally seen as a compactification of M_B = M\M' by vector bundles (on support).
Keywords
Cite
@article{arxiv.1103.1485,
title = {Universal plane curve and moduli spaces of 1-dimensional coherent sheaves},
author = {Oleksandr Iena},
journal= {arXiv preprint arXiv:1103.1485},
year = {2014}
}
Comments
Added references, some typos corrected. Incorporated referee's suggestions. A similar version of the paper has been accepted to Communications in Algebra