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On vector bundles over reducible curves with a node
Advances in Geometry ( IF 0.5 ) Pub Date : 2020-07-26 , DOI: 10.1515/advgeom-2020-0010
Filippo F. Favale 1 , Sonia Brivio 1
Affiliation  

Let $C$ be a curve with two smooth components and a single node. Let $\mathcal{U}_C(r,w,\chi)$ be the moduli space of $w$-semistable classes of depth one sheaves on $C$ having rank $r$ on both components and Euler characteristic $\chi$. In this paper, under suitable assumptions, we produce a projective bundle over the product of the moduli spaces of semistable vector bundles of rank $r$ on each components and we show that it is birational to an irreducible component of $\mathcal{U}_C(r,w,\chi)$. Then we prove the rationality of the closed subset containing vector bundles with given fixed determinant.

中文翻译:

关于具有节点的可约曲线上的向量丛

令 $C$ 是一条具有两个平滑分量和一个节点的曲线。令 $\mathcal{U}_C(r,w,\chi)$ 是 $w$-半稳态深度类的模空间,在 $C$ 上的一个层在两个分量和欧拉特征 $\chi 上都具有秩 $r$ $. 在本文中,在适当的假设下,我们在每个分量上的秩为 $r$ 的半稳定向量丛的模空间的乘积上产生一个射影丛,并且我们证明它对 $\mathcal{U} 的不可约分量是双有理的_C(r,w,\chi)$。然后我们证明了包含给定固定行列式的向量丛的闭子集的合理性。
更新日期:2020-07-26
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