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

Aleksei Lavrov

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

Algebraic Geometry 2020-12-11 v1

Authors: Aleksei Lavrov

Abstract

In the present paper we describe new component of the Gieseker-Maruyama moduli space $\mathcal{M}(14)$ of coherent semistable rank-2 sheaves with Chern classes $c_1=0, \ c_2=14, \ c_3=0$ on $\mathbb{P}^{3}$ 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.

Keywords

moduli space semistable sheaves non-reduced component elementary transformation hilbert scheme projective space

Cite

@article{arxiv.2012.05611,
  title  = {A new non-reduced moduli component of rank 2 semistable sheaves on P3},
  author = {Aleksei Lavrov},
  journal= {arXiv preprint arXiv:2012.05611},
  year   = {2020}
}

Comments

20 pages. arXiv admin note: text overlap with arXiv:1903.00772

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