Brown, Gavin D.
(2007)
*
Fano 3-folds with divisible anticanonical class.
*
Manuscripta Mathematica,
123
(1).
pp. 37-51.
ISSN 0025-2611.
(doi:10.1007/s00229-007-0082-6)
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Official URL http://dx.doi.org/10.1007/s00229-007-0082-6 |

## 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, 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.

Item Type: | Article |
---|---|

DOI/Identification number: | 10.1007/s00229-007-0082-6 |

Subjects: | Q Science > QA Mathematics (inc Computing science) |

Divisions: |
Faculties > Sciences > School of Mathematics Statistics and Actuarial Science Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics |

Depositing User: | G.D. Brown |

Date Deposited: | 31 Mar 2008 09:24 UTC |

Last Modified: | 28 May 2019 13:37 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/2420 (The current URI for this page, for reference purposes) |

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