Classification of logarithmic Fano threefolds

Hironobu Maeda

Compositio Mathematica (1986)

  • Volume: 57, Issue: 1, page 81-125
  • ISSN: 0010-437X

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Maeda, Hironobu. "Classification of logarithmic Fano threefolds." Compositio Mathematica 57.1 (1986): 81-125. <http://eudml.org/doc/89751>.

@article{Maeda1986,
author = {Maeda, Hironobu},
journal = {Compositio Mathematica},
keywords = {classification; logarithmic Fano threefolds; extremal rational curves; ampleness},
language = {eng},
number = {1},
pages = {81-125},
publisher = {Martinus Nijhoff Publishers},
title = {Classification of logarithmic Fano threefolds},
url = {http://eudml.org/doc/89751},
volume = {57},
year = {1986},
}

TY - JOUR
AU - Maeda, Hironobu
TI - Classification of logarithmic Fano threefolds
JO - Compositio Mathematica
PY - 1986
PB - Martinus Nijhoff Publishers
VL - 57
IS - 1
SP - 81
EP - 125
LA - eng
KW - classification; logarithmic Fano threefolds; extremal rational curves; ampleness
UR - http://eudml.org/doc/89751
ER -

References

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  2. [2] I.V. Dëmin: Addemdum to the paper "Fano 3-folds representable in the form of line bundles". Math. USSR Izvestija20 (1983) 625-626. Zbl0536.14026
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  5. [5] R. Hartshorne: Algebraic Geometry. GTM52, Springer (1977). Zbl0367.14001MR463157
  6. [6] S. Iitaka: Algebraic Geometry: An Introduction to Birational Geometry of Algebraic Varieties. GTM76, Springer (1981). Zbl0491.14006MR637060
  7. [7] S. Iitaka: Birational Geometry for Open Algebraic Varieties. Montreal UP76 (1981). Zbl0491.14005MR647148
  8. [8] V.A. Iskovskih: Anticanonical models of three dimensional algebraic varieties. J. Soviet Math.13 (1980) 815-868. Zbl0428.14016
  9. [9] V.A. Iskovskih: Treedimensional Fano varities. I, II. Math. USSR Izvestija11 (1977) 485-527, Zbl0382.14013
  10. ibid., 12 (1978) 469-509. 
  11. [10] K. Kodaira: On stability of compact submanifolds of complex manifolds. Amer. J. Math.85 (1963) 79-94. Zbl0173.33101MR153033
  12. [11] S.L. Kleiman: Toward a numberical theory of ampleness. Ann. of Math.84 (1966) 293-344. Zbl0146.17001MR206009
  13. [12] H. Maeda: On certain ampleness criteria for divisors on threefolds. Preprint (1983). 
  14. [13] Y.I. Manin: Cubic Forms: Algebra, Geometry, Arithmetic. North-Holland (1974). Zbl0277.14014MR833513
  15. [14] M. Miyanishi: Algebraic methods in the theory of algebraic threefolds. In: Algebraic Varieties and Analytic Varities, Advanced Studies in Pure Mathematics. 1. North-HollandKinokuniya (1983). Zbl0537.14027MR715647
  16. [15] S. Mori: Threefolds whose canonical bundles are not numerically effectie. Ann. of Math.116 (1982) 133-176. Zbl0557.14021MR662120
  17. [16] S. Mori and S. Mukai: Classifications of 3-folds with B2 ≽ 2. Manuscripta Math.36 (1981) 147-162. Zbl0478.14033
  18. [17] S. Mori and S. Mukai: On Fano 3-folds with B2 ≽ 2. In: Algebraic Varieties and Analytic Varieties, Advanced Studies in Pure Math. 1. North-HollandKinokuniya (1983). Zbl0537.14026
  19. [18] J.P. Murre: Classification of Fano threefolds according to Fano and Iskovskih. In: Algebraic Threefolds: Lect. Notes in Math. 947. Springer (1981). Zbl0492.14025MR672614
  20. [19] Y. Norimatsu: Kodaira vanishing theorem and Chern classes for ∂-manifolds. Proc. J. Acad.54 (1978) 107-108. Zbl0433.32013
  21. [20] N. Nygaard: On the fundamental group of uni-rational 3-fold. Invent. math.44 (1978) 75-86. Zbl0427.14014MR491731
  22. [21] M. Reid: Lines on Fano 3-folds according to Shokurov. Mittag-Leffler Report No. 11 (1980). 
  23. [22] S. Tsunoda: Open surfaces of logarithmic Kodaira dimension - ∞. Talk at Seminar on Analytic Manifolds, Univ. of Tokyo (1981). 
  24. [23] S. Tsunoda and M. Miyanishi: The structure of open algebraic surfaces. II. In : Classification of Algebraic and Analytic Manifolds. Progress in Mathematics39. Birkäuser (1983). Zbl0605.14035MR728617
  25. [24] H. Umemura and S. Mukai: Minimal rational threefolds. In: Algebraic Geometry. Lect. Notes in Math.1016. Springer (1983) Zbl0526.14006MR726439

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