Fano 3-folds with divisible anticanonical class

Brown, G.D. (2007) Fano 3-folds with divisible anticanonical class. Manuscripta Mathematica, 123 (1). pp. 37-51. ISSN 0025-2611. (The full text of this publication is not available from this repository)

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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
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Pure Mathematics
Depositing User: G.D. Brown
Date Deposited: 31 Mar 2008 09:24
Last Modified: 14 Jan 2010 14:06
Resource URI: http://kar.kent.ac.uk/id/eprint/2420 (The current URI for this page, for reference purposes)
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