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manuscripta mathematica

, Volume 123, Issue 1, pp 37–51 | Cite as

Fano 3-folds with divisible anticanonical class

  • Gavin Brown
  • Kaori Suzuki
Article

Abstract

We show the nonvanishing of H 0(X,−K X ) for any a Fano 3-fold X for which −K X is a multiple of another Weil divisor in Cl(X). The main case we study is Fano 3-folds with Fano index 2: that is, 3-folds X with rank Pic(X)=1, \({\mathbb{Q}}\) -factorial terminal singularities and −K X  = 2A for an ample Weil divisor A. We give a first classification of all possible Hilbert series of such polarised varieties (X,A) and deduce both the nonvanishing of H 0(X,−K X ) and the sharp bound (−K X )3≥ 8/165. We find the families that can be realised in codimension up to 4.

Mathematics Subject Classification (2000)

Primary 14J30 Secondary 14E30 14Q15 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.IMSASUniversity of KentCanterburyUK
  2. 2.Tokyo Institute of TechnologyMeguro-kuJapan

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