Kodaira dimension and zeros of holomorphic one-forms

By Mihnea Cristian Popa, C. Schnell. 2012

52 citations recorded by the source corpus.

We show that every holomorphic one-form on a smooth complex projective variety of general type must vanish at some point. The proof uses generic vanishing theory for Hodge modules on abelian varieties.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9a76e23aff59a3f6aeb41fc39f153907fa5be2b6

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In Geometry and Topology

1. Mihnea Cristian Popa
2. C. Schnell
3. M. Mustaţă
4. Nero Budur

In Mathematical Physics

1. Mihnea Cristian Popa
2. C. Schnell
3. M. Mustaţă
4. Nero Budur

Citations in the corpus

• Viehweg’s hyperbolicity conjecture for families with maximal variation (2015, methodology): “ •⊆ grFM of the associated graded of the underlying filtered DXmodule (M,F•M). This is constructed in Theorem 9.2. In the case when X is an abelian variety, this type of construction was considered in [PS14]. We prove and use a slightly stronger version of Theorem C involving such submodules; see The”