3 papers
math.AG2024
Hodge modules and Kähler morphisms
Mads Bach Villadsen
We prove the decomposition theorem for Hodge modules with integral structure along proper Kähler morphisms, partially generalizing M. Saito's theorem for projective morphisms. Our…
math.AG2021
Kodaira dimension and zeros of holomorphic one-forms, revisited
Mads Bach Villadsen
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…
math.AG2020
Chen-Jiang decompositions for projective varieties, without Hodge modules
Mads Bach Villadsen
We give a new proof of a theorem by Pareschi, Popa and Schnell that the direct image of the canonical bundle of a smooth projective variety along a morphism to an abelian variety a…