Kodaira dimension and zeros of holomorphic one-forms, revisited

DOI10.4310/MRL.2022.V29.N6.A12zbMATH Open1517.32053arXiv2102.08347OpenAlexW3131208190MaRDI QIDQ6043373

Mads Bach Villadsen

Publication date: 5 May 2023

Published in: Mathematical Research Letters (Search for Journal in Brave)

Abstract: We give a new proof that every holomorphic one-form on a smooth complex projective variety of general type must vanish at some point, first proven by Popa and Schnell using generic vanishing theorems for Hodge modules. Our proof relies on Simpson's results on the relation between rank one Higgs bundles and local systems of one-dimensional complex vectors spaces, and the structure of the cohomology jump loci in their moduli spaces.

Full work available at URL: https://arxiv.org/abs/2102.08347

zbMATH Keywords

Higgs bundlesholomorphic one-formsmooth complex projective variety of general type

Mathematics Subject Classification ID

Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30) Holomorphic bundles and generalizations (32L05)

Related Items (3)

Logarithmic Kodaira dimension and zeros of holomorphic log-one-forms ⋮ Zeros of Holomorphic One-Forms and Topology of Kähler Manifolds ⋮ Deformations of the trivial line bundle and vanishing theorems

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