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Fano manifolds of index n-1 and the cone conjecture

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posted on 2015-07-13, 13:17 authored by Izzet Coskun, Artie PrendergastArtie Prendergast
The Morrison-Kawamata cone conjecture predicts that the actions of the automorphism group on the effective nef cone and the pseudo-automorphism group on the effective movable cone of a klt Calabi-Yau pair (X,Δ) have finite, rational polyhedral fundamental domains. Let Z be an n-dimensional Fano manifold of index n-1 such that -KZ=(n-1)H for an ample divisor H. Let Γ be the base locus of a general (n-1)-dimensional linear system V ⊂/H/. In this paper, we verify the Morrison-Kawamata cone conjecture for the blowup of Z along Γ. © 2013 The Author(s). Published by Oxford University Press. All rights reserved.

Funding

During the preparation of this article the first author was partially supported by the NSF CAREER grant DMS-0950951535, and an Alfred P. Sloan Foundation Fellowship.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

International Mathematics Research Notices

Volume

2014

Issue

9

Pages

2401 - 2439

Citation

COSKUN, I. and PRENDERGAST-SMITH, A., 2014. Fano manifolds of index n-1 and the cone conjecture. International Mathematics Research Notices, (9), pp.2401-2439

Publisher

Oxford University Press / © The Authors

Version

  • AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2014

Notes

This is a pre-copyedited, author-produced PDF of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record is available online at: http://dx.doi.org/10.1093/imrn/rns297

ISSN

1073-7928

eISSN

1687-0247

Language

  • en

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