Seshadri constants on Bott towers

TL;DR

This paper computes Seshadri constants for nef line bundles on Bott towers, providing explicit values at any point under certain conditions, advancing understanding of positivity in algebraic geometry.

Contribution

It offers explicit calculations of Seshadri constants on Bott towers, a class of iterated projective bundles, under specific conditions, which was previously not well-understood.

Findings

Explicit formulas for Seshadri constants on Bott towers

Conditions under which the calculations hold

Enhanced understanding of line bundle positivity on complex varieties

Abstract

For a positive integer $n$, let $X_n \to X_{n-1} \to \ldots \to X_2 \to X_1 \to X_0$ be a Bott tower of height $n$, and let $L$ be a nef line bundle on $X_n$. We compute Seshadri constants $\varepsilon(X_n,L,x)$ of $L$ at any point $x \in X_n$ under some conditions.