arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2208.03210math.AG
收藏

三重Fano上的瞬时层

Instanton sheaves on Fano threefolds

Gaia Comaschi, Marcos Jardim

摘要:

推广最初由库兹涅佐夫和Faenzi提出的定义,我们研究(可能非局部自由)瞬子层的任意秩的Fano三倍。我们对秩为1的瞬子层进行了分类,并描述了所有结构层为秩为0的瞬子层的曲线。此外,我们还证明了每一个秩为2的瞬子层都是局部自由瞬子层沿秩为0的瞬子层的初等变换。为了完成本文,我们描述了二次三重$X$上电荷为2的秩为2的瞬子层的模空间,并证明了具有陈类$(c_1,c_2,c_3)=(-1,2,0)$的$X$上秩为2的半稳定层的全模空间是连通的,并且除了瞬子分量外,只包含另一个也被完全描述的不可约分量.

英文摘要:

Generalizing the definitions originally presented by Kuznetsov and Faenzi, we study (possibly non locally free) instanton sheaves of arbitrary rank on Fano threefolds. We classify rank 1 instanton sheaves and describe all curves whose structure sheaves are rank 0 instanton sheaves. In addition, we show that every rank 2 instanton sheaf is an elementary transformation of a locally free instanton sheaf along a rank 0 instanton sheaf. To complete the paper, we describe the moduli space of rank 2 instanton sheaves of charge 2 on a quadric threefold $X$, and show that the full moduli space of rank 2 semistable sheaves on $X$ with Chern classes $(c_1,c_2,c_3)=(-1,2,0)$ is connected and contains, besides the instanton component, just one other irreducible component which is also fully described.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑