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arXiv · 2203.07007

On pseudoeffective cones of projective bundles and volume function

Snehajit Misra·Anoop Singh
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Abstract

In this article, we compute the pseudo-effective cones of various projective bundles $\mathbb{P}_X(E)$ over higher dimensional varieties $X$ under some assumptions on $X$ as well as on the vector bundle $E$. We also compute the volume function on fibre product $\mathbb{P}(E)\times_C\mathbb{P}(F)$ of two projective bundles over a smooth irreducible complex projective curve $C$. In particular, we show that the volume function on the fiber product of two ruled surfaces is of polynomial type.

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Snehajit Misra, Anoop Singh. 2022-03-14. On pseudoeffective cones of projective bundles and volume function. https://arxiv.org/abs/2203.07007

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