SISSA Open Science

# Moduli space of pairs over projective stacks

 dc.contributor.author Andreini, Elena dc.date.accessioned 2012-01-23T16:10:05Z dc.date.available 2012-01-23T16:10:05Z dc.date.issued 2011-05-27 dc.identifier.uri http://preprints.sissa.it/xmlui/handle/1963/5263 dc.description.abstract Let $\clX$ a projective stack over an algebraically closed field $k$ of en_US characteristic 0. Let $\clE$ be a generating sheaf over $\clX$ and $\clO_X(1)$ a polarization of its coarse moduli space $X$. We define a notion of pair which is the datum of a non vanishing morphism $\Gamma\otimes\clE\to \clF$ where $\Gamma$ is a finite dimensional $k$ vector space and $\clF$ is a coherent sheaf over $\clX$. We construct the stack and the moduli space of semistable pairs. The notion of semistability depends on a polynomial parameter and it is dictated by the GIT construction of the moduli space. dc.language.iso en en_US dc.publisher SISSA en_US dc.relation.ispartofseries arXiv:1105.5637v1; dc.title Moduli space of pairs over projective stacks en_US dc.type Preprint en_US dc.subject.miur MAT/03 GEOMETRIA dc.contributor.department Mathematical Physics en_US dc.miur.area 1 en_US dc.contributor.area Mathematics en_US
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