L²-type Dolbeault isomorphisms and vanishing theorems for logarithmic sheaves twisted by multiplier ideal sheaves

2022/11/18 by Watanabe, Yuta
#14F17 #14F18 #32L10 #32L20 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.10077

Abstract

In this article, we first establish an L²-type Dolbeault isomorphism for the sheaf of logarithmic differential forms twisted by the multiplier ideal sheaf. By using this isomorphism and L²-estimates equipped with a singular Hermitian metric, we obtain logarithmic vanishing theorems involving multiplier ideal sheaves on compact Kähler manifolds with simple normal crossing divisors.

Related

• Logarithmic vanishing theorems on compact Kähler manifolds I
• L²-Dolbeault resolution of the lowest Hodge piece of a Hodge module
• A Le Potier-type isomorphism twisted with multiplier submodule sheaves
• Vanishing theorems for Dolbeault cohomology of log homogeneous varieties
• Logarithmic forms with twisted coefficients