Strong generic vanishing and a higher-dimensional Castelnuovo–de Franchis inequality
Giuseppe Pareschi and Mihnea Popa
Source: Duke Math. J. Volume 150, Number 2 (2009), 269-285.
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 on the Evans-Griffith syzygy theorem in commutative algebra. Along the way we give a positive answer, in the setting of Kähler manifolds, to a question of Green and Lazarsfeld on the vanishing of higher direct images of Poincaré bundles. We indicate generalizations to arbitrary integral transforms
Primary Subjects: 14J40, 14F17
Secondary Subjects: 14K12
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1255699341
Digital Object Identifier: doi:10.1215/00127094-2009-051
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