Vanishing Theorem for the de Rham Complex of Unitary Local System
Hongshan Li
TL;DR
This paper proves a vanishing theorem for the logarithmic de Rham complex of unitary local systems, extending classical results and analyzing the weight filtration to establish stronger graded complex properties.
Contribution
It introduces a Kodaira-Nakano type vanishing theorem for the logarithmic de Rham complex of unitary local systems and studies the associated weight filtration.
Findings
Proved a vanishing theorem for the logarithmic de Rham complex
Analyzed the weight filtration on the complex
Established stronger results for the associated graded complex
Abstract
We will prove a Kodaira-Nakano type of vanishing theorem for the logarithmic de Rham complex of unitary local system. We will then study the weight filtration on the logarithmic de Rham complex, and prove a stronger statement for the associated graded complex.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Topics in Algebra · Algebraic Geometry and Number Theory