On pseudoeffective thresholds and cohomology of twisted symmetric tensor fields on irreducible Hermitian symmetric spaces

Abstract

Let $X$ be an irreducible Hermitian symmetric space of compact type (IHSS for short). In this paper, we give the irreducible decomposition of $Sy{m}^r{T}_X$. As a by-product, we give a cohomological characterization of the rank of $X$. Moreover, we introduce pseudoeffective thresholds to measure the bigness of tangent bundles of smooth complex projective varieties precisely and calculate them for irreducible Hermitian symmetric spaces of compact type.

Corrected a minor error in Remark 5.12 of the published version

References in corpus (2)

• Cohomological characterizations of projective spaces and hyperquadrics
• Bigness of the tangent bundle of del Pezzo surfaces and $D$-simplicity

Cited by in corpus (1)

• Bigness of the tangent bundle of a Fano threefold with Picard number two