A vanishing theorem for log canonical pairs
arXiv:0805.3863
Abstract
Using inversion of adjunction, we deduce from Nadel's theorem a vanishing property for ideals sheaves on projective varieties, a special case of which recovers a result due to Bertram--Ein--Lazarsfeld. This enables us to generalize to a large class of projective schemes certain bounds on Castelnuovo--Mumford regularity previously obtained by Bertram--Ein--Lazarsfeld in the smooth case and by Chardin--Ulrich for locally complete intersection varieties with rational singularities. Our results are tested on several examples.
arXiv comment15 pages; v3: minor changes, to appear in Amer. J. Math; v4: as pointed out to us by Victor Lozovanu, we need to assume that the line bundle A in Theorem 1.1 is ample, instead of just nef and big; this change does not affect any of the other results