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Nef cone and seshadri constants of product of projective bundles of any dimension over curves

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Nef cone and Seshadri constants of product of projective bundles of any dimension over curves. Preprint .... Nef cone of flag bundles over a curve. Article.

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Nef cone and Seshadri constants of product of projective bundles of any dimension over curves

Preprint · December 2018 with 57 Reads · Download citation

Rupam Karmakar

1.92

- The Institute of Mathematical Sciences

Snehajit Misra

1.92

- Tata Institute of Fundamental Research

Abstract

Let $X = \mathbb{P}(E_1) \times_C \mathbb{P}(E_2)$ where $C$ is a smooth curve and $E_1$, $E_2$ are vector bundles over $C$. Here we calculate the nef cone of $X$, where $E_1$ and $E_2$ are unstable vector bundles of rank $r_1$ and $r_2$ respectively and in the case where $E_1$ is semistable vector bundle of rank $r_1$ and $E_2$ is unstable vector bundle of rank $r_2$. We also calculate the Seshadri constants of ample line bundles on $X$.