Brown, G.D. (2007) Fano 3-folds with divisible anticanonical class. Manuscripta Mathematica, 123 (1). pp. 37-51. ISSN 0025-2611.
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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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