Q-divisor and Ampleness

TL;DR

This paper introduces two new criteria for determining the ampleness of divisors on complex smooth projective varieties, utilizing multiplier ideal sheaves and the model category framework.

Contribution

It provides novel criteria for ampleness based on multiplier ideal sheaves and the model category, advancing the understanding of divisor positivity.

Findings

Criteria for ampleness using multiplier ideal sheaves

Criteria for ampleness using the model category

Enhanced tools for algebraic geometers to verify ampleness

Abstract

We give two criteria for a divisor on complex smooth projective variety to be ample using the multiplier ideal sheaf and the model category.