Moduli space of pairs over projective stacks

2011/05/27 by Elena Andreini, Andreini, Elena
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1105.5637

openalex publication_date 2011/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \clX a projective stack over an algebraically closed field k of 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 Γ⊗\clE→ \clF where Γ 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.

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