An Inductive Approach to Basepoint-Freeness of Adjoint Series on Irregular Varietiess

TL;DR

This paper introduces an inductive method to establish basepoint-freeness of linear systems on irregular varieties, proving Fujita's conjecture for certain cases assuming lower-dimensional cases are known.

Contribution

It presents a novel inductive approach to prove basepoint-freeness on irregular varieties, extending Fujita's conjecture under mild conditions.

Findings

Proves Fujita's conjecture for irregular varieties with nef anticanonical bundle in certain cases.

Develops an inductive framework applicable to higher-dimensional irregular varieties.

Establishes basepoint-freeness assuming lower-dimensional cases are verified.

Abstract

In this paper, we show how to prove the basepoint-freeness for linear systems on irregular varieties inductively. For instance, we prove that Fujita's conjecture holds for irregular varieties of dimension $\mathnormal{n}$ with a nef anticanonical bundle assuming it holds for lower-dimensional varieties and under mild conditions.