Publications of the Research Institute for Mathematical Sciences· 2026Q2
Kollár’s Package for Polystable Locally Abelian Parabolic Higgs Bundles
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- Q2SCImago
- 2026year
Short summary
Researchers extend Kollár's package (torsion-freeness, injectivity, vanishing, decomposition theorems) to polystable locally abelian parabolic Higgs bundles, offering a unified framework for complex geometry.
AI-generated from the title and abstract; the full text is not read.
Key points
- Generalizes Kollár's package to polystable locally abelian parabolic Higgs bundles.
- Introduces a multiplier ideal sheaf associated with an R-divisor for twisted bundles.
- Provides a uniform treatment for diverse Kollár's package applications in complex geometry.
- Deduces weak positivity and generic vanishing for higher direct image sheaves as applications.
AI-generated from the title and abstract; the full text is not read.
Abstract
We generalize Kollár’s package (including torsion-freeness, injectivity theorem, vanishing theorem and decomposition theorem) to polystable locally abelian parabolic Higgs bundles twisted by a multiplier ideal sheaf associated with an \mathbb{R} -divisor. This gives a uniform treatment for various kinds of Kollár’s package in different topics in complex geometry. As applications, the weak positivity (in the sense of Viehweg) and the generic vanishing property for higher direct image sheaves are deduced.
The authors' abstract, as published at the source. Publications of the Research Institute for Mathematical Sciences, 2026 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics