The Nonvanishing problem for varieties with nef anticanonical bundle

Abstract

We prove that if $(X,\Delta )$ is a threefold pair with mild singularities such that $-(K_X+\Delta )$ is nef, then the numerical class of $-(K_X+\Delta )$ is effective.

arXiv commentv4: minor changes; to appear in Doc. Math

References in corpus (11)

• Klt varieties with trivial canonical class -- Holonomy, differential forms, and fundamental groups
• On Generalised Abundance, I
• Abundance for varieties with many differential forms
• On the existence of minimal models for log canonical pairs
• Projectively flat KLT varieties
• On Generalised Abundance, II
• A note on the abundance conjecture
• Special MMP for log canonical generalised pairs
• Structure theorem for projective klt pairs with nef anti-canonical divisor
• On a numerical criterion for Fano fourfolds
• Rationally connected threefolds with nef and bad anticanonical divisor

Cited by in corpus (4)

• Miyaoka type inequality for terminal threefolds with nef anti-canonical divisors
• Remarks on the existence of minimal models of log canonical generalized pairs
• Algebraic fibre spaces with strictly nef relative anti-log canonical divisor
• Two Non-Vanishing results concerning the Anti-Canonical Bundle