DOI QR코드

DOI QR Code

ANTI-FLIPS OF THE BLOW-UPS OF THE PROJECTIVE SPACES AT TORUS INVARIANT POINTS

  • Hiroshi Sato (Department of Applied Mathematics Faculty of Sciences Fukuoka University) ;
  • Shigehito Tsuzuki (Department of Applied Mathematics Faculty of Sciences Fukuoka University)
  • 투고 : 2022.12.21
  • 심사 : 2023.05.16
  • 발행 : 2023.11.30

초록

We explicitly construct the smooth toric Fano variety which is isomorphic to the blow-up of the projective space at torus invariant points in codimension one by anti-flips.

키워드

과제정보

The first author was partly supported by JSPS KAKENHI Grant Number JP18K03262.

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. L. Bonavero, Toric varieties whose blow-up at a point is Fano, Tohoku Math. J. (2) 54 (2002), no. 4, 593-597. http://projecteuclid.org/euclid.tmj/1113247651 https://doi.org/10.2748/tmj/1113247651
  4. D. A. Cox, J. B. Little, and H. Schenck, Toric varieties, Graduate Studies in Mathematics, 124, Amer. Math. Soc., Providence, RI, 2011. https://doi.org/10.1090/gsm/124
  5. G. Ewald, On the classification of toric Fano varieties, Discrete Comput. Geom. 3 (1988), no. 1, 49-54. https://doi.org/10.1007/BF02187895
  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 Univ. Press, Princeton, NJ, 1993. https://doi.org/10.1515/9781400882526
  8. K. Matsuki, Introduction to the Mori Program, Universitext, Springer, New York, 2002. https://doi.org/10.1007/978-1-4757-5602-9
  9. T. Oda, Convex bodies and algebraic geometry, translated from the Japanese, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 15, Springer, Berlin, 1988.
  10. M. Reid, Decomposition of toric morphisms, in Arithmetic and geometry, Vol. II, 395-418, Progr. Math., 36, Birkhauser Boston, Boston, MA, 1983.
  11. H. Sato, 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
  12. V. E. Voskresenskij and A. A. Klyachko, Toroidal Fano varieties and root systems, Math. USSR-Izv. 24 (1985), 221-244. https://doi.org/10.1070/IM1985v024n02ABEH001229