Freeness of adjoint linear systems on threefolds with terminal Gorenstein singularities or some quotient singularities

1998/12/24 by Nobuyuki Kakimi, Kakimi, Nobuyuki · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/9812139

21 pages, Latex

openalex publication_date 1998/12/24 · arxiv created 2000/04/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Fujita-type freeness for quasi-log canonical threefolds
• Freeness of adjoint linear systems on threefolds with non Gorenstein Q-factorial terminal singularities or some quotient singularities

Related

• Freeness of adjoint linear systems on threefolds with non Gorenstein Q-factorial terminal singularities or some quotient singularities
• Fujita-type freeness for quasi-log canonical threefolds
• Fujita's Freeness Conjecture for T-Varieties of Complexity One
• On the multiplicity of terminal singularities on threefolds
• On Fujita's freeness conjecture for 3-folds and 4-folds