On generalized nefness and bigness in adjunction theory

TL;DR

This paper explores the conditions under which certain adjoint divisors, formed from positive line bundles and canonical divisors, are effective and ample, advancing understanding in the field of algebraic geometry.

Contribution

It provides new criteria for the effectiveness and ampleness of adjoint divisors involving generalized nefness and bigness in adjunction theory.

Findings

Criteria for effectiveness of adjoint divisors

Conditions for ampleness of adjoint divisors

Enhanced understanding of positivity properties in algebraic geometry

Abstract

We investigate effectiveness and ampleness of adjoint divisors of the form $aL+bK_X$, where $L$ is a suitably positive line bundle on a smooth projective variety $X$ and $a,b$ are positive integers.