Email this article A new series of moduli components of rank-2 semistable sheaves on $\mathbb{P}^{3}$ with singularities of mixed dimension
- Authors: Ivanov A.N.1
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Affiliations:
- Department of Mathematics, National Research University "Higher School of Economics"
- Issue: Vol 211, No 7 (2020)
- Pages: 72-92
- Section: Articles
- URL: https://journal-vniispk.ru/0368-8666/article/view/133338
- DOI: https://doi.org/10.4213/sm9312
- ID: 133338
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Abstract
We construct a new infinite series of irreducible components of the Gieseker-Maruyama moduli scheme $\mathscr{M}(k)$, $k \geq 3$, of semistable rank-2 sheaves on $\mathbb{P}^3$ with Chern classes $c_1=0$, $c_2=k$ and $c_3=0$, whose general points are sheaves with singularities of mixed dimension. These sheaves are constructed by elementary transformations of stable and properly $\mu$-semistable reflexive sheaves along disjoint unions of collections of points and smooth irreducible curves which are rational or complete intersection curves in $\mathbb{P}^{3}$. As a special member of this series, we obtain a new component of $\mathscr{M}(3)$. Bibliography: 12 titles.
About the authors
Aleksei Nikolaevich Ivanov
Department of Mathematics, National Research University "Higher School of Economics"without scientific degree, no status
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