Universal plane curve and moduli spaces of 1-dimensional coherent sheaves

Details Universal plane curve and moduli spaces of 1-dimensional coherent sheaves Universal plane curve and moduli spaces of 1-dimensional coherent sheaves

2011-03-08

arxiv.org/abs/1103.1485v1

Mathematics

Algebraic Geometry

Scientific paper

We show that the universal plane curve M of degree d may be seen as a space of isomorphism classes of certain 1-dimensional coherent sheaves on the projective plane. The universal singular locus M' of M 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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