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Title: The cone conjecture for some rational elliptic threefolds
Authors: Prendergast-Smith, Artie
Issue Date: 2012
Publisher: © Springer-Verlag
Citation: PRENDERGAST-SMITH, A., 2012. The cone conjecture for some rational elliptic threefolds. Mathematische Zeitschrift, 272 (1-2), pp. 589 - 605.
Abstract: A central problem of modern minimal model theory is to describe the various cones of divisors associated to a projective variety. For Fano varieties the nef cone and movable cone are rational polyhedral by the cone theorem [4, Theorem 3.7] and the theorem of Birkar– Cascini–Hacon–McKernan [1]. For more general varieties the picture is much less clear: these cones need not be rational polyhedral, and can even have uncountably many extremal rays. The Morrison-Kawamata cone conjecture [8, 3, 13] describes the action of automorphisms on the cone of nef divisors and the action of pseudo-automorphisms on the cone of movable divisors, in the case of a Calabi-Yau variety, a Calabi-Yau fibre space, or a Calabi-Yau pair. Although these cones need not be rational polyhedral, the conjecture predicts that they should have a rational polyhedral fundamental domain for the action of the appropriate group. It is not clear where these automorphisms or pseudo-automorphisms should come from; nevertheless, the conjecture has been proved in various contexts by Sterk–Looijenga– Namikawa [11, 9] Kawamata [3], and Totaro [14]. In this paper we give some new evidence for the conjecture, by verifying it for some threefolds which are blowups of P3 in the base locus of a net (that is, a 2-dimensional linear system) of quadrics.
Description: This article was submitted for publication in the journal, Mathematische Zeitschrift [© Springer-Verlag]. The final publication is available at Springer via http://dx.doi.org/10.1007/s00209-011-0951-2
Version: Submitted for publication
DOI: 10.1007/s00209-011-0951-2
URI: https://dspace.lboro.ac.uk/2134/18240
Publisher Link: http://dx.doi.org/10.1007/s00209-011-0951-2
ISSN: 0025-5874
Appears in Collections:Published Articles (Maths)

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