Freeness of adjoint linear systems on threefolds with terminal Gorenstein singularities or some quotient singularities
Algebraic Geometry
2007-05-23 v2
Abstract
We generalize the result of Kawamata concerning the strong version of Fujita's freeness conjecture for smooth 3-folds to some singular cases, namely, Gorenstein terminal singularities and quotient singularities of type 1/r(1,1,1) and of type 1/r(1,1,-1). We generalize furthermore the result of that to projective threefolds with only canonical singularities for canonical and not terminal singularities. It turns out that the estimates in the first three cases are better than the one for the smooth case, which it is not in the fourth case. We also give explicit examples which show the estimate in the fourth case is necessarily worse than the one for the smooth case.
Keywords
Cite
@article{arxiv.math/9812139,
title = {Freeness of adjoint linear systems on threefolds with terminal Gorenstein singularities or some quotient singularities},
author = {Nobuyuki Kakimi},
journal= {arXiv preprint arXiv:math/9812139},
year = {2007}
}
Comments
21 pages, Latex