Nagoya Mathematical Journal

Classification of non-Gorenstein ${\bf Q}$-Fano $d$-folds of Fano index greater than $d-2$

Takeshi Sano

Full-text: Open access

Article information

Source
Nagoya Math. J., Volume 142 (1996), 133-143.

Dates
First available in Project Euclid: 14 June 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1118772046

Mathematical Reviews number (MathSciNet)
MR1399470

Zentralblatt MATH identifier
0864.14023

Subjects
Primary: 14J45: Fano varieties

Citation

Sano, Takeshi. Classification of non-Gorenstein ${\bf Q}$-Fano $d$-folds of Fano index greater than $d-2$. Nagoya Math. J. 142 (1996), 133--143. https://projecteuclid.org/euclid.nmj/1118772046


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References

  • [Al] Alexeev, V. A., Theorem about good divisors on log Fano varieties, Lecture Notes in Math., 1479(Springer Verlag 1989), 1-9.
  • [Do] Dolgachev, I., Weighted projective varieties, in Group action and vector fields, Lecture Notes in Math., 956(Springer Verlag 1982), 3 4 - 7 1.
  • [Fl] Fletcher, A. R., Working with weighted complete intersections, MPI/89-35 Univ. of Warwick Thesis, 1989.
  • [Ful] Fujita, T., Classification theories of polarized varieties, London Math. Soc. Lec- ture Note Series, 155, 1990.
  • [Fu2] Fujita, On singular Del Pezzo varieties, in Algebraic Geometry, Lecture Notes in Math., 1417(Springer Verlag 1990), 117-128.
  • [H] Hartshorne, R., Algebraic Geometry, Graduate Texts in Math, 52 (Springer Var- lag 1977).
  • [HW] Hidaka, H. and Watanabe, K., Normal Gorenstein surface with ample anti- canonical divisor, Tokyo J. Math., 4 (1981), 319-330.
  • [Isl] Iskovskih, V. A., Fano threefolds I, (English translation) Math. USSR Izvestija, 11 (1977), 485-527.
  • [Is2] Iskovskih, Fano threefolds II, (English translation) Math. USSR Izvestija, 12 (1978), 469-506.
  • [Kal] Kawamata, Y., On plurigenera of minimal algebraic 3-folds with K 0, Math. Ann., 275 (1986), 539-546.
  • [Ka2] Kawamata, Boundedness of Q-Fano threefolds, Proc. of the Int. Conf. on Algebra, Part 3 (Novosibirsk 1989), 439-445, Contemp. Math., 131, Part 3, Amer. Math. Soc, Providence, RI, 1992.
  • [KMM] Kawamata, Matsuda, K. and Matsuki, K. Introduction to the minimal model problem, Adv. Stud, in Pure Math., 10 (1987), 283-360.
  • [Mo] Mori, S., On a generalization of complete intersections, J. Math. Kyoto Univ., 15-3(1975), 619-646.
  • [MM] and Mukai, S., Classification of Fano 3-fold with B2 2, Manuscripta Math., 36(1981), 147-162.
  • [Mu] Mukai, S., Biregular classification of Fano 3-folds and Fano manifolds of coin- dex 3, Proc. Natl. Acad. Sci. USA, Vol. 86, 3000-3002, May 1989.
  • [Re] Reid, M., Young person's guide to canonical singularities, in Algebraic Geomet- ry Bowdoin (1985), part I, pp. 345-414, Proc. of Symp. in Pure Math., 46, A. M. S., 1987.
  • [Shi] Shokurov, V. V., Smoothness of the general anticanonical divisor on a Fano 3-fold, (English translation) Math. USSR Izvestija, 14 (1980), 395-405.
  • [Sh2] Shokurov, The existence of a straight line on Fano 3-folds, (English translation) Math. USSR, Izvestija, 15 (1980), No. 1, 173-209. Graduate School of Polymathematics Nagoya University Nagoya 464-01, Japan