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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Galindo, C. and Monserrat, F. 2016. The cone of curves and the Cox ring of rational surfaces given by divisorial valuations. Advances in Mathematics, Vol. 290, p. 1040.


    González, José Hering, Milena Payne, Sam and Süß, Hendrik 2012. Cox rings and pseudoeffective cones of projectivized toric vector bundles. Algebra & Number Theory, Vol. 6, Issue. 5, p. 995.


    Prendergast-Smith, Arthur 2012. The cone conjecture for some rational elliptic threefolds. Mathematische Zeitschrift, Vol. 272, Issue. 1-2, p. 589.


    Artebani, Michela and Laface, Antonio 2011. Cox rings of surfaces and the anticanonical Iitaka dimension. Advances in Mathematics, Vol. 226, Issue. 6, p. 5252.


    Testa, Damiano Várilly-Alvarado, Anthony and Velasco, Mauricio 2011. Big rational surfaces. Mathematische Annalen, Vol. 351, Issue. 1, p. 95.


    Birkar, Caucher 2010. On termination of log flips in dimension four. Mathematische Annalen, Vol. 346, Issue. 2, p. 251.


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Hilbert’s 14th problem over finite fields and a conjecture on the cone of curves

  • Burt Totaro (a1)
  • DOI: http://dx.doi.org/10.1112/S0010437X08003667
  • Published online: 01 September 2008
Abstract
Abstract

We give the first examples over finite fields of rings of invariants that are not finitely generated. (The examples work over arbitrary fields, for example the rational numbers.) The group involved can be as small as three copies of the additive group. The failure of finite generation comes from certain elliptic fibrations or abelian surface fibrations having positive Mordell–Weil rank. Our work suggests a generalization of the Morrison–Kawamata cone conjecture on Calabi–Yau fiber spaces to klt Calabi–Yau pairs. We prove the conjecture in dimension two under the assumption that the anticanonical bundle is semi-ample.

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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
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