Steenbrink vanishing theorem for big line bundles

2026/08/02 by Yuta Watanabe
Mathematics · #math.CV #msc:32L20 #msc:14F17 #msc:32S20 #msc:14F18 #msc:32J25 #msc:32C15

paper · pdf

16 pages

arxiv created 2026/08/02 · arxiv updated 2026/08/04

Abstract

In this paper, we generalize the Steenbrink vanishing theorem for ample line bundles on complex projective varieties by extending it to big line bundles on compact complex spaces with multiplier ideal sheaves.

Citations

• L²-Dolbeault resolutions and Nadel vanishing on weakly pseudoconvex complex spaces with singular Hermitian metrics
• Bigness of adjoint linear subsystem and approximation theorems with ideal sheaves on weakly pseudoconvex manifolds
• L²-type Dolbeault isomorphisms and vanishing theorems for logarithmic sheaves twisted by multiplier ideal sheaves
• Nakano-Nadel type, Bogomolov-Sommese type vanishing and singular dual Nakano semi-positivity
• Bogomolov-Sommese type vanishing theorem for holomorphic vector bundles equipped with positive singular Hermitian metrics
• Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I