Reference : Universal plane curves and Simpson moduli spaces of 1-dimensional sheaves
Scientific congresses, symposiums and conference proceedings : Poster
Physical, chemical, mathematical & earth Sciences : Mathematics
Universal plane curves and Simpson moduli spaces of 1-dimensional sheaves
Iena, Oleksandr mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
1st Joint Conference of the Belgian, Royal Spanish and Luxembourg Mathematical Societies
from 6-6-2012 to 8-6-2012
University of Liege
[en] Simpson moduli spaces ; coherent sheaves ; vector bundles on curves
[en] 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).
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