D -dimensions of algebraic surfaces and numerically effective divisors

Fumio Sakai

Compositio Mathematica (1983)

  • Volume: 48, Issue: 1, page 101-118
  • ISSN: 0010-437X

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Sakai, Fumio. "$D$-dimensions of algebraic surfaces and numerically effective divisors." Compositio Mathematica 48.1 (1983): 101-118. <http://eudml.org/doc/89582>.

@article{Sakai1983,
author = {Sakai, Fumio},
journal = {Compositio Mathematica},
keywords = {D-dimensions of algebraic surfaces; numerically effective divisors; Kodaira dimension},
language = {eng},
number = {1},
pages = {101-118},
publisher = {Martinus Nijhoff Publishers},
title = {$D$-dimensions of algebraic surfaces and numerically effective divisors},
url = {http://eudml.org/doc/89582},
volume = {48},
year = {1983},
}

TY - JOUR
AU - Sakai, Fumio
TI - $D$-dimensions of algebraic surfaces and numerically effective divisors
JO - Compositio Mathematica
PY - 1983
PB - Martinus Nijhoff Publishers
VL - 48
IS - 1
SP - 101
EP - 118
LA - eng
KW - D-dimensions of algebraic surfaces; numerically effective divisors; Kodaira dimension
UR - http://eudml.org/doc/89582
ER -

References

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  1. [1] M. Artin and G. Winters: Degenerate fibres and stable reduction of curves. Topology10 (1971) 373-383. Zbl0196.24403MR476756
  2. [2] E. Bombieri and Mumford: Enriques' classification of surfaces in char. p. II, III. Complex Analysis and Algebraic Geometry. Iwanami and Cambridge Univ. Press, Tokyo and Cambridge (1977) 207-217, Inventiones math.36 (1976) 197-232. Zbl0336.14010MR491719
  3. [3] M. Demazure: Anneaux gradués normaux. Séminaire sur les singularités des surfaces. Ecole Polytechnique1979. 
  4. [4] T. Fujita: On Zariski problem. Proc. Japan Acad.55, Ser. A (1979) 106-110. Zbl0444.14026MR531454
  5. [5] S. Iitaka: On D-dimensions of algebraic varieties. J. Math. Soc. Japan23 (1971) 356-373. Zbl0212.53802MR285531
  6. [6] Y. Kawamata: Addition formula of logarithmic Kodaira dimensions for morphisms of relative dimension one. Int. Symp. Algebraic Geometry Kyoto1977. Kinokuniya, Tokyo (1978) 207-217. Zbl0437.14018MR578860
  7. [7] Y. Kawamata: On classification of non-complete algebraic surfaces. Lecture Notes in Mathematics732. Springer; Berlin, Heidelberg, New York (1979) 215-232. Zbl0407.14012MR555700
  8. [8] S.L. Kieiman: Toward a numerical theory of ampleness. Ann. of Math.84 (1966) 293-344. Zbl0146.17001MR206009
  9. [9] M. Miyanishi: On Non-complete Algebraic Surfaces. Lecture Notes in Mathematics857. Springer; Berlin, Heidelberg, New York, 1981. Zbl0456.14018
  10. [10] D. Mumford: Enriques classification of surfaces in char. p. I. Global Analysis. Tokyo Univ. Press and Princeton Univ. Press, Tokyo and Princeton (1969) 325-339. Zbl0188.53201MR254053
  11. [11] F. Sakai: Semi-stable curves on algebraic surfaces and logarithmic pluricanonical maps. Math. Ann.254 (1980) 89-120. Zbl0431.14011MR597076
  12. [12] F. Sakai: Curves with trivial dualizing sheaf on algebraic surfaces. (To appear in Amer. J. Math.) Zbl0512.14021MR681735
  13. [13] F. Sakai: Enriques classification of normal Gorenstein surfaces. (To appear in Amer. J. Math.) Zbl0512.14022MR681736
  14. [14] F. Sakai: Anti-Kodaira dimension of ruled surfaces. Sci. Rep. Saitama Univ.10 (1982) 1-7. Zbl0496.14022MR662405
  15. [15] O. Zariski: The theorem of Riemann-Roch for high multiples of an effective divisor on an algebraic surface. Ann. of Math.76 (1962) 560-615. Zbl0124.37001MR141668

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