Strong generic vanishing and a higher-dimensional Castelnuovo–de Franchis inequality

By Giuseppe Pareschi, Mihnea Cristian Popa. 2008

61 citations recorded by the source corpus.

We extend to manifolds of arbitrary dimension the Castelnuovo-de Franchis inequality for surfaces. The proof is based on the theory of Generic Vanishing and higher regularity, and on the Evans-Griffith Syzygy Theorem in commutative algebra. Along the way we give a positive answer, in the setting of Kahler manifolds, to a question of Green-Lazarsfeld on the vanishing of higher direct images of Poincare' bundles. We indicate generalizations to arbitrary Fourier-Mukai transforms.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4eb4bed4b30a5abf8b2029bc7e68bd1405d185fd

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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

• GENERIC VANISHING THEORY VIA MIXED HODGE MODULES (2011, methodology): “Fourier–Mukai transform of OX conjectured by Green and Lazarsfeld, and proved by Hacon [14] (and in the Kähler setting in [26]).”