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A functorial construction of moduli of sheaves

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Abstract

We show how natural functors from the category of coherent sheaves on a projective scheme to categories of Kronecker modules can be used to construct moduli spaces of semistable sheaves. This construction simplifies or clarifies technical aspects of existing constructions and yields new simpler definitions of theta functions, about which more complete results can be proved.

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Authors and Affiliations

  1. Instituto de Matemáticas y Física Fundamental, Consejo Superior de Investigaciones Científicas, Serrano 113 bis, 28006, Madrid, Spain

    Luis Álvarez-Cónsul

  2. Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK

    Alastair King

Authors
  1. Luis Álvarez-Cónsul
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  2. Alastair King
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Correspondence to Alastair King.

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Dedicated to the memory of Joseph Le Potier.

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Álvarez-Cónsul, L., King, A. A functorial construction of moduli of sheaves. Invent. math. 168, 613–666 (2007). https://doi.org/10.1007/s00222-007-0042-5

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  • DOI: https://doi.org/10.1007/s00222-007-0042-5

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