A new non-reduced moduli component of rank 2 semistable sheaves on P3

2020/12/10 by Aleksei Lavrov, Lavrov, Aleksei
Mathematics · #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.2012.05611

openalex publication_date 2020/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper we describe new component of the Gieseker-Maruyama moduli space M(14) of coherent semistable rank-2 sheaves with Chern classes c₁=0, c₂=14, c₃=0 on ℙ³ which is generically non-reduced. The construction of this component is based on the technique of elementary transformations of sheaves and famous Mumford's example of a non-reduced component of the Hilbert scheme of smooth space curves of degree 14 and genus 24.

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