Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Vanishing theorem for tame harmonic bundles via $L^2$-cohomology (1912.02586v2)

Published 5 Dec 2019 in math.AG and math.CV

Abstract: Using $L2$-methods, we prove a vanishing theorem for tame harmonic bundles over quasi-compact K\"ahler manifolds in a very general setting. As a special case, we give a completely new proof of the Kodaira type vanishing theorems for Higgs bundles due to Arapura. To prove our vanishing theorem, we construct a fine resolution of the Dolbeault complex for tame harmonic bundles via the complex of sheaves of $L2$-forms, and we establish the H\"ormander $L2$-estimate and solve $(\bar{\partial}_E+\theta)$-equations for Higgs bundles $(E,\theta)$.

Summary

We haven't generated a summary for this paper yet.