Higher dimensional examples of manifolds whose adjoint bundles are not spanned

1996/03/28 by Takeshi Kawachi, Kawachi, Takeshi
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9603023

TeX-Type: AmS-TeX 2.1, 6 pages

arxiv created 1996/03/28 · arxiv updated 2009/11/30

Abstract

Let (X,L) be an n-dimensional polarized variety. Fujita's conjecture says that if Lⁿ>1 then the adjoint bundle K_X+nL is spanned and K_X+(n+1)L is very ample. There are some examples such that K_X+nL is not spanned or K_X+(n+1)L is not very ample. These are (¶ⁿ,Ø(1)), hypersurface M of degree 6 in weighted projective space ¶(3,2,1,1,⋯ ,1) with Ø_M(1) and numerically Godeaux surface etc. Numerically Godeaux surface is the quotient space of a Fermat type hypersurface of degree 5 in ¶³ by an action of order 5. These examples are not so much. We construct new examples for any dimention.

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