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.
Pareschi, G., Popa, M. (2009). Strong generic vanishing and a higher dimensional Calstelnuovo-de Franchis inequality. DUKE MATHEMATICAL JOURNAL, 150(2), 269-285 [10.1215/00127094-2009-051].
Strong generic vanishing and a higher dimensional Calstelnuovo-de Franchis inequality
PARESCHI, GIUSEPPE;
2009-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
