On effective non-vanishing and base-point-freeness

TL;DR

This paper investigates conditions under which certain divisors on log terminal varieties have non-zero global sections, providing new results particularly in lower-dimensional cases.

Contribution

It offers new criteria for non-vanishing and base-point-freeness of divisors on log terminal varieties, especially in lower dimensions.

Findings

Established non-vanishing results for divisors on log terminal varieties in lower dimensions

Provided conditions ensuring base-point-freeness of divisors

Extended previous results to broader classes of varieties

Abstract

Let $X$ be a complete normal variety, $B$ an effective $\mathbb{R}$-divisor on $X$, and $D$ a Cartier divisor on $X$. Assume that the pair $(X, B)$ is log terminal. We consider the problem whether $H^0(X, D) \ne 0$ and obtain some results in lower dimensions.