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arXiv · 2001.01207

Existence of semistable vector bundles with fixed determinants

Inder Kaur
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Abstract

Let $R$ be an excellent Henselian discrete valuation ring with algebraically closed residue field $k$ of any characteristic. Fix integers $r,d$ with $r\ge 2$. Let $X_R$ be a regular fibred surface over Spec($R$) with special fibre denoted $X_k$, a generalised tree-like curve of genus $g \ge 2$. Let ${L}_R$ be a line bundle on $X_R$ of degree $d$ such that the degree of the restriction of ${L}_R$ on the rational components of $X_k$ is a multiple of $r$. In this article we prove the existence of a rank $r$ locally free sheaf on $X_R$ of determinant ${L}_R$ such that it is semistable on the fibres.

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Inder Kaur. 2020-01-05. Existence of semistable vector bundles with fixed determinants. https://doi.org/10.1016/j.geomphys.2018.12.023

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