Positive cones of $b$-divisor classes

Snehajit Misra; Nabanita Ray

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arXiv · 2509.25948

Positive cones of $b$-divisor classes

Snehajit Misra·Nabanita Ray

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Abstract

In this article, we define the notion of ample Cartier $b$-divisor classes by using the notion of Seshadri constants for Cartier $b$-divisor classes. In particular, we have shown that the set of all ample Cartier $b$-divisor classes forms a convex cone inside the nef cone of Cartier $b$-divisor classes. Furthermore, we have studied various properties of these Cartier ample $b$-divisor classes. We have also given an equivalent characterization of big Cartier $b$-divisor classes in terms of volume function of the pseudo-effective Cartier $b$-divisor classes. More specifically, we prove that the set of all big Cartier $b$-divisor classes form a convex cone. Finally we have investigated how the nef Cartier $b$-divisor classes behave under the pullback.

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Snehajit Misra, Nabanita Ray. 2025-09-30. Positive cones of $b$-divisor classes. https://arxiv.org/abs/2509.25948

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