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The Log Minimal Model Program for Horospherical Varieties Via Moment Polytopes

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Abstract

In a previous work, we described the Minimal Model Program in the family of ℚ-Gorenstein projective horospherical varieties, by studying certain continuous changes of moment polytopes of polarized horospherical varieties. Here, we summarize the results of the previous work and we explain how to generalize them in order to describe the Log Minimal Model Program for pairs (X, Δ) when X is a projective horospherical variety.

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References

  1. Brion, M.: Groupe de picard et nombres caractéristiques des variétés sphériques. Duke Math. J., 58 (2), 397–424 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  2. Brion, M.: Variétés sphériques et théorie de Mori. Duke Math. J., 72 (2), 369–404 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  3. Fujino, O.: What is log terminal? In Flips for 3-folds and 4-folds, volume 35 of Oxford Lecture, Ser. Math. Appl., 49–62, Oxford Univ. Press, Oxford, 2007

    Google Scholar 

  4. Knop, F.: The Luna–Vust theory of spherical embeddings. In Proceedings of the Hyderabad Conference on Algebraic Groups (Hyderabad, 1989), 225–249, Manoj Prakashan, Madras, 1991

    MATH  Google Scholar 

  5. Kollár, J., Mori, S.: Birational geometry of algebraic varieties, volume 134 of Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge, 1998. With the collaboration of C. H. Clemens and A. Corti, Translated from the 1998 Japanese original

  6. Pasquier, B.: Variétés horosphériques de Fano. PhD thesis, Université Joseph Fourier, Grenoble 1, available at http://tel.archives-ouvertes.fr/tel-00111912, 2006

    MATH  Google Scholar 

  7. Pasquier, B.: Variétés horosphériques de Fano. Bull. Soc. Math. France, 136 (2), 195–225 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Pasquier, B.: A Minimal Model Program for Q-Gorenstein varieties. preprint available at arXiv: 1406.6005v2, 2014

    Google Scholar 

  9. Pasquier, B.: An approach of the minimal model program for horospherical varieties via moment polytopes. J. Reine Angew. Math., 708, 173–212 (2015)

    MathSciNet  MATH  Google Scholar 

  10. Pasquier, B.: KLT singularities of horospherical pairs. Ann. Inst. Fourier (Grenoble), 66 (5), 2157–2167 (2016)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The author would like to thank the referee for his wise comments that improved the quality of the paper.

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Authors and Affiliations

  1. Institut Montpelliérain Alexander Grothendieck, CNRS, Univ. Montpellier, CC 51-Place Eugène Bataillon, 34095, Montpellier cedex 5, France

    Boris Pasquier

  2. Laboratoire de Mathématiques et Applications, CNRS, Université de Poitiers, Téléport 2, 11 boulevard Marie et Pierre Curie, 86962, Chasseneuil Futuroscope Cedex, France

    Boris Pasquier

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  1. Boris Pasquier
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Correspondence to Boris Pasquier.

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Pasquier, B. The Log Minimal Model Program for Horospherical Varieties Via Moment Polytopes. Acta. Math. Sin.-English Ser. 34, 542–562 (2018). https://doi.org/10.1007/s10114-017-6558-8

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  • DOI: https://doi.org/10.1007/s10114-017-6558-8

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