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

Kodaira dimension and zeros of holomorphic one-forms, revisited