# Toric vector bundles on Bott tower

## TL;DR

This paper investigates the properties of toric vector bundles on Bott towers, providing criteria for positivity, semi-stability, and ampleness, and characterizing line bundles using Bott numbers.

## Contribution

It offers new criteria for s-jet ampleness, nefness, and big line bundles, and characterizes semi-stable toric vector bundles with discriminant zero on Bott towers.

## Key findings

- Criteria for s-jet ampleness of line bundles
- Characterization of nef and big line bundles using Bott numbers
- Conditions for ampleness of semi-stable toric vector bundles

## Abstract

In this paper, using Klyachko's classification theorem we study positivity and semi-stability of toric vector bundles on a class of nonsingular projective toric varieties, known as Bott towers. In particular, we give a criterion of $s$-jet ampleness of line bundles and characterize nef and big line bundles on Bott towers using Bott numbers. We obtain a criterion for the ampleness of discriminant zero semi-stable toric vector bundles on nonsingular projective varieties. We also describe toric subbundles of toric vector bundles on nonsingular toric varieties.