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Mathematics > Algebraic Geometry

arXiv:1812.03957 (math)
[Submitted on 10 Dec 2018 (v1), last revised 29 Feb 2020 (this version, v2)]

Title:Nef cone and Seshadri constants on products of projective bundles over curves

Authors:Rupam Karmakar, Snehajit Misra
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Abstract:Let $X = \mathbb{P}(E_1) \times_C \mathbb{P}(E_2)$ where $C$ is a smooth curve and let $E_1$, $E_2$ be vector bundles over $C$. In this paper, we extend the results in \cite{K-M-R} by computing the nef cone of $X$ without restriction on the rank or semistability of $E_1$ and $E_2$. We also study the Seshadri constants of ample line bundles on $X$. We calculate the Seshadri constants in some cases and give bounds in some of the remaining cases.
Comments: Final version. To appear in Journal of Ramanujan Mathematical Society
Subjects: Algebraic Geometry (math.AG)
Cite as: arXiv:1812.03957 [math.AG]
  (or arXiv:1812.03957v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1812.03957

Submission history

From: Rupam Karmakar [view email]
[v1] Mon, 10 Dec 2018 18:10:16 UTC (10 KB)
[v2] Sat, 29 Feb 2020 07:37:42 UTC (11 KB)
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