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The cone conjecture for some rational elliptic threefolds

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References

  1. Birkar C., Cascini P., Hacon C., McKernan J.: Existence of minimal models for varieties of log general type. J. Am. Math. Soc. 23(2), 405–468 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Hartshorne R.: Algebraic Geometry. Springer, New York (1977)

    MATH  Google Scholar 

  3. Kawamata Y.: On the cone of divisors of Calabi–Yau fiber spaces. Int. J. Math. 8, 665–687 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  4. Kollár J., Mori S.: Birational Geometry of Algebraic Varieties. Cambridge University Press, Cambridge (1998)

    Book  MATH  Google Scholar 

  5. Lazarsfeld R.: Positivity in Algebraic Geometry. I. Springer, Berlin (2004)

    Book  Google Scholar 

  6. Looijenga, E.: Discrete automorphism groups of convex cones of finite type. arXiv:0908.0165

  7. Mori S.: Threefolds whose canonical bundles are not numerically effective. Ann. Math. 116, 133–176 (1982)

    Article  MATH  Google Scholar 

  8. Morrison D.: Compactifications of moduli spaces inspired by mirror symmetry. Journées de géométrie algébrique d’Orsay (Orsay, Astérisque) 218, 243–271 (1993)

    Google Scholar 

  9. Namikawa Y.: Periods of Enriques surfaces. Math. Ann. 270, 201–222 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  10. Oguiso K.: On the finiteness of fiber-space structures on a Calabi–Yau 3-fold. J. Math. Sci. 106, 3320–3335 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  11. Sterk H.: Finiteness results for algebraic K3 surfaces. Math. Z. 189, 507–513 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  12. Szendröi B.: Some finiteness results for Calabi–Yau threefolds. J. Lond. Math. Soc. 60, 689–699 (1999)

    Article  MATH  Google Scholar 

  13. Totaro B.: Hilbert’s fourteenth problem over finite fields, and a conjecture on the cone of curves. Compos. Math. 144(5), 1176–1198 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Totaro B.: The cone conjecture for Calabi–Yau pairs in dimension two. Duke Math. J. 154, 241–263 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. Uehara H.: Calabi–Yau threefolds with infinitely many divisorial contractions. J. Math. Kyoto Univ. 44, 99–118 (2004)

    MathSciNet  MATH  Google Scholar 

  16. Wilson, P.M.H.: Minimal models of Calabi–Yau threefolds. Classification of algebraic varieties (L’Aquila, 1992), pp. 403–410

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  1. Arthur Prendergast-Smith

    Present address: Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL, 60607, USA

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  1. Leibniz Universität Hannover, Institut für Algebraische Geometrie, Welfengarten 1, 30167, Hannover, Germany

    Arthur Prendergast-Smith

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  1. Arthur Prendergast-Smith
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Correspondence to Arthur Prendergast-Smith.

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Prendergast-Smith, A. The cone conjecture for some rational elliptic threefolds. Math. Z. 272, 589–605 (2012). https://doi.org/10.1007/s00209-011-0951-2

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  • DOI: https://doi.org/10.1007/s00209-011-0951-2

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