L² representation of Simpson-Mochizuki's prolongation of Higgs bundles and the Kawamata-Viehweg vanishing theorem for semistable parabolic Higgs bundles

2022/10/09 by Chen Zhao, Zhao, Chen
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2210.04130

openalex publication_date 2022/10/09 · openalex created_date 2022/10/12 · openalex updated_date 2026/07/28

Abstract

In this paper, we provide an L² fine resolution of the prolongation of a nilpotent harmonic bundle in the sense of Simpson-Mochizuki (an analytic analogue of the Kashiwara-Malgrange filtrations). This is the logarithmic analogue of Cattani-Kaplan-Schmid's and Kashiwara-Kawai's results on the L² interpretation of the intersection complex. As an application, we give an L²-theoretic proof to the Nadel-Kawamata-Viehweg vanishing theorem with coefficients in a nilpotent Higgs bundle.

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