Freeness of Adjoint Linear Systems on Threefolds with Terminal Gorenstein Singularities or Some Quotient Singularities
Vol. 7 (2000), No. 3, Page 347--368.
Kakimi, Nobuyuki
Freeness of Adjoint Linear Systems on Threefolds with Terminal Gorenstein Singularities or Some Quotient Singularities
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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, Gorenstein ${\mathbb Q}$-factorial 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, while 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.
Mathematics Subject Classification (1991): Primary 14C20; Secondary 14J30
Mathematical Reviews Number: MR1792732
Received: 1999-01-13
