대한수학회지 (Journal of the Korean Mathematical Society)

  • 제58권5호
  • /
  • Pages.1081-1107
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  • 2021
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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A SUFFICIENT CONDITION FOR A TORIC WEAK FANO 4-FOLD TO BE DEFORMED TO A FANO MANIFOLD

  • Sato, Hiroshi (Department of Applied Mathematics Faculty of Sciences Fukuoka University)
  • 투고 : 2019.12.04
  • 심사 : 2021.05.25
  • 발행 : 2021.09.01
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초록

In this paper, we introduce the notion of toric special weak Fano manifolds, which have only special primitive crepant contractions. We study their structure, and in particular completely classify smooth toric special weak Fano 4-folds. As a result, we can confirm that almost every smooth toric special weak Fano 4-fold is a weakened Fano manifold, that is, a weak Fano manifold which can be deformed to a Fano manifold.

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참고문헌

  1. V. V. Batyrev, On the classification of smooth projective toric varieties, Tohoku Math. J. (2) 43 (1991), no. 4, 569-585. https://doi.org/10.2748/tmj/1178227429
  2. V. V. Batyrev, On the classification of toric Fano 4-folds, J. Math. Sci. (New York) 94 (1999), no. 1, 1021-1050. https://doi.org/10.1007/BF02367245
  3. C. Casagrande, Contractible classes in toric varieties, Math. Z. 243 (2003), no. 1, 99-126. https://doi.org/10.1007/s00209-002-0453-3
  4. D. A. Cox, J. B. Little, and H. K. Schenck, Toric varieties, Graduate Studies in Mathematics, 124, American Mathematical Society, Providence, RI, 2011. https://doi.org/10.1090/gsm/124
  5. O. Fujino, Notes on toric varieties from Mori theoretic viewpoint, Tohoku Math. J. (2) 55 (2003), no. 4, 551-564. http://projecteuclid.org/euclid.tmj/1113247130 https://doi.org/10.2748/tmj/1113247130
  6. O. Fujino and H. Sato, Introduction to the toric Mori theory, Michigan Math. J. 52 (2004), no. 3, 649-665. https://doi.org/10.1307/mmj/1100623418
  7. W. Fulton, Introduction to Toric Varieties, Annals of Mathematics Studies, 131, Princeton University Press, Princeton, NJ, 1993. https://doi.org/10.1515/9781400882526
  8. R. Koelman, The number of moduli of families of curves on toric surfaces, Thesis, Univ. Nijmegen, 1991.
  9. A. Laface and M. Melo, On deformations of toric varieties, preprint, arXiv:1610.03455.
  10. K. Matsuki, Introduction to the Mori program, Universitext, Springer-Verlag, New York, 2002. https://doi.org/10.1007/978-1-4757-5602-9
  11. T. Minagawa, On classification of weakened Fano 3-folds with B2(X) = 2, in Proc. of Algebraic Geometry Symposium, Kinosaki, Oct. 2000.
  12. T. Minagawa, Global smoothing of singular weak Fano 3-folds, J. Math. Soc. Japan 55 (2003), no. 3, 695-711. https://doi.org/10.2969/jmsj/1191418998
  13. T. Oda, Convex bodies and algebraic geometry, translated from the Japanese, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 15, Springer-Verlag, Berlin, 1988.
  14. M. Reid, Decomposition of toric morphisms, in Arithmetic and geometry, Vol. II, 395-418, Progr. Math., 36, Birkhauser Boston, Boston, MA, 1983.
  15. M. Reid, Toward the classification of higher-dimensional toric Fano varieties, Tohoku Math. J. (2) 52 (2000), no. 3, 383-413. https://doi.org/10.2748/tmj/1178207820
  16. M. Reid, The classification of smooth toric weakened Fano 3-folds, Manuscripta Math. 109 (2002), no. 1, 73-84. https://doi.org/10.1007/s002290200289
  17. H. Sato and Y. Suyama, Remarks on toric manifolds whose Chern characters are positive, Comm. Algebra 48 (2020), no. 6, 2528-2538. https://doi.org/10.1080/00927872.2020.1719412