A global description of the fine Simpson moduli space of 1-dimensional sheaves supported on plane quartics

2016/07/05 by Oleksandr Iena, Iena, Oleksandr
Mathematics · #14D20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1607.01319

openalex created_date 2016/06/24 · openalex publication_date 2016/07/05 · openalex updated_date 2026/07/28

Abstract

A global description of the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics is given: we describe the gluing of the Brill-Noether loci described by Drézet and Maican and show that the Simpson moduli space M=M_{4m± 1}(\mathbb P₂) is a blow-down of a blow-up of a projective bundle over a smooth moduli space of Kronecker modules. An easy computation of the Poincaré polynomial of M is presented.

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