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Some birational maps of Fano 3-folds

Kiyohiko Takeuchi

Compositio Mathematica (1989)

  • Volume: 71, Issue: 3, page 265-283
  • ISSN: 0010-437X

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Takeuchi, Kiyohiko. "Some birational maps of Fano 3-folds." Compositio Mathematica 71.3 (1989): 265-283. <http://eudml.org/doc/89976>.

@article{Takeuchi1989,
author = {Takeuchi, Kiyohiko},
journal = {Compositio Mathematica},
keywords = {classification of Fano 3-folds; extremal ray; genus},
language = {eng},
number = {3},
pages = {265-283},
publisher = {Kluwer Academic Publishers},
title = {Some birational maps of Fano 3-folds},
url = {http://eudml.org/doc/89976},
volume = {71},
year = {1989},
}

TY - JOUR
AU - Takeuchi, Kiyohiko
TI - Some birational maps of Fano 3-folds
JO - Compositio Mathematica
PY - 1989
PB - Kluwer Academic Publishers
VL - 71
IS - 3
SP - 265
EP - 283
LA - eng
KW - classification of Fano 3-folds; extremal ray; genus
UR - http://eudml.org/doc/89976
ER -

References

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  1. 0. E. Bombieri and H.P.F. Swinnerton-Dyer, On the local zeta function of a cubic threefold, Ann. Scuola Norm. Pisa(3) 211-29 (1967). Zbl0153.50501MR212019
  2. 1. V.A. Iskovskih, Fano 3-folds I, Izv. Akad. Nauk SSSR Ser. Mat.41 (1977) 516-562; English transl. in Math. USSR Izv.11 (1977) 485-527. Zbl0382.14013MR463151
  3. 2. V.A. Iskovskih, Fano 3-folds II, Izv. Akad. Nauk SSSR Ser. Mat.42 (1978) 506-549; English transl. in Math. USSR Izv.12 (1978) 469-506. Zbl0407.14016MR503430
  4. 3. V.A. Iskovakih, Anticanonical models of three-dimensional algebraic varieties, Itogi Nauki i Tekniki, Sovremennye Problemy Matematiki, 12 (1979) 59-157; English transl. in J. Soviet Math.13 (1980) 745-814. Zbl0428.14016MR537685
  5. 4. V.A. Iskovskih, Birational automorphisms of three-dimensional algebraic varieties, Itogi Nauki i Tekhniki, Sovremennye Problemy Matematiki, 12 (1979) 159-236; English transl. in J. Soviet Math.13 (1980) 815-868. Zbl0428.14017MR537686
  6. 5. J. Kollár, Flops, to appear in Nagoya Math. J. Zbl0645.14004MR986434
  7. 6. S. Mori, Lecture on extremal rays and Fano 3-folds, Nagoya University, Fall Term 1983-84. 
  8. 7. S. Mori and S. Mukai, On Fano 3-folds with B2 ≽ 2, Advanced Studies in Pure Math.1, Algebraic Varieties and Analytic Varieties, 101-129 (1983). Zbl0537.14026
  9. 8. S. Mori and S. Mukai, Classification of Fano 3-folds with B2 ≽ 2, I, Algebraic and Topological Theories - to the memory of Dr. Takehiko MIYATA, 496-545 (1985). Zbl0800.14021
  10. 9. M. Reid, Minimal models of canonical 3-folds, Advanced Studies in Pure Math.1, Algebraic Varieties and Analytic Varieties, 131-180 (1983). Zbl0558.14028MR715649
  11. 10. M. Reid, Lines on Fano 3-folds according to Shokurov, Report 11 (1980) Mittag-Leffler Institute. 
  12. 11. V.V. Shokurov, The existence of a straight line on Fano 3-folds, Izv. Akad. Nauk SSSR Ser. Mat.43 (1979) 921-963; English transl. in Math. USSR Izv.15 (1980) 173-209. Zbl0444.14027
  13. 12. A.N. Tjurin, The geometry of the Fano surface of the nonsingular cubic F c P4 and Torelli's theorems for Fano surfaces and cubics, Izv. Akad. Nauk SSSR Ser. Mat.35 (1971) 498-529; English transl. in Math. USSR Izv.5 (1971) 517-546. Zbl0252.14004MR285539

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