Fano 3-folds with divisible anticanonical class

• Autores: Gavin Brown , Kaori Suzuki
• Localización: Manuscripta mathematica, ISSN 0025-2611, Vol. 123, Nº. 1, 2007, págs. 37-51
• Idioma: inglés
• DOI: 10.1007/s00229-007-0082-6
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• Resumen

  • 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, -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.