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

Pareschi, Giuseppe; Popa, Mihnea

Duke Math. J., Tome 146 (2009) no. 1, p. 269-285 / Harvested from Project Euclid

Résumé

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

Publié le : 2009-11-01
Classification: 14J40, 14F17, 14K12

@article{1255699341,
     author = {Pareschi, Giuseppe and Popa, Mihnea},
     title = {Strong generic vanishing and a higher-dimensional Castelnuovo--de Franchis inequality},
     journal = {Duke Math. J.},
     volume = {146},
     number = {1},
     year = {2009},
     pages = { 269-285},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1255699341}
}

Pareschi, Giuseppe; Popa, Mihnea. Strong generic vanishing and a higher-dimensional Castelnuovo–de Franchis inequality. Duke Math. J., Tome 146 (2009) no. 1, pp.  269-285. http://gdmltest.u-ga.fr/item/1255699341/