On the canonical ring of algebraic varieties

P. M. H. Wilson

Compositio Mathematica (1981)

  • Volume: 43, Issue: 3, page 365-385
  • ISSN: 0010-437X

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Wilson, P. M. H.. "On the canonical ring of algebraic varieties." Compositio Mathematica 43.3 (1981): 365-385. <http://eudml.org/doc/89507>.

@article{Wilson1981,
author = {Wilson, P. M. H.},
journal = {Compositio Mathematica},
keywords = {canonical model; divisor; threefold of general type; Gorenstein threefold; finite generation of canonical ring},
language = {eng},
number = {3},
pages = {365-385},
publisher = {Sijthoff et Noordhoff International Publishers},
title = {On the canonical ring of algebraic varieties},
url = {http://eudml.org/doc/89507},
volume = {43},
year = {1981},
}

TY - JOUR
AU - Wilson, P. M. H.
TI - On the canonical ring of algebraic varieties
JO - Compositio Mathematica
PY - 1981
PB - Sijthoff et Noordhoff International Publishers
VL - 43
IS - 3
SP - 365
EP - 385
LA - eng
KW - canonical model; divisor; threefold of general type; Gorenstein threefold; finite generation of canonical ring
UR - http://eudml.org/doc/89507
ER -

References

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  2. [2] E. Bombieri: Canonical models of surfaces of general type. Publ. IHES.42 (1973) 447-495. Zbl0259.14005MR318163
  3. [3] J.E. Goodman: Affine open subsets of algebraic varieties and ample divisors. Ann. of Math.89 (1969) 160-183. Zbl0159.50504MR242843
  4. [4] H. Grauert and O. Riemenschneider: Verschwindungssätze für analytische Kohomologiegruppen auf komplexen Räumen. Inventiones math.11 (1970) 263-292. Zbl0202.07602MR302938
  5. [5] R. Hartshorne: Ample subvarieties of algebraic varieties. Lecture Notes in Mathematics156. Berlin, Heidelberg, New York: Springer1977. Zbl0208.48901MR282977
  6. [6] H. Hironaka: Resolution of singularities of an algebraic variety over a field of characteristic zero. Ann. of Math.79 (1964) 109-326. Zbl0122.38603MR199184
  7. [7] S. Iitaka: On D-dimensions of algebraic varieties. J. Math. Soc. Japan23 (1971) 356-373. Zbl0212.53802MR285531
  8. [8] Y. Kawamata: On the classification of non-complete algebraic surfaces. Proc. Summer Meeting on Algebraic Geometry, Copenhagen1978, pages 215-232. Lecture Notes in Mathematics732. Berlin, Heidelberg, New York: Springer1979. Zbl0407.14012MR555700
  9. [9] S.L. Kleiman: Towards a numerical theory of ampleness. Ann. of Math.84 (1966) 293-344. Zbl0146.17001MR206009
  10. [10] S. Mori: Threefolds whose canonical bundles are not numerically effective. Proc. Nat. Acad. Sci. USA77 (1980) 3125-3126. Zbl0434.14022MR574383
  11. [11] D. Mumford: The topology of normal singularities of an algebraic surface and a criterion for simplicity. Publ. IHES9 (1961) 5-22. Zbl0108.16801MR153682
  12. [12] H. Popp: Moduli theory and classification theory of algebraic varieties. Lecture Notes in Mathematics620. Berlin, Héidelberg, New York: Springer1977. Zbl0359.14005MR466143
  13. [13] C.P. Ramanujam: Supplement to the article "Remarks on the Kodaira Vanishing Theorem". J. Indian Math. Soc.38 (1974) 121-124. Zbl0368.14005MR393048
  14. [14] M.A. Reid: Canonical 3-folds; to appear in: Journées de Géométrie Algébrique, Juillet 1979, edited by A. Beauville. Sijthoff & Noordhoff1980. Zbl0451.14014MR605332
  15. [15] K. Ueno: On the pluricanonical systems on algebraic manifolds. Math. Ann216 (1975) 173-179. Zbl0293.14003MR402130
  16. [16] P.M.H. Wilson: The behaviour of the plurigenera of surfaces under algebraic smooth deformations. Inventiones math.47 (1978) 289-299. Zbl0371.14017MR501373
  17. [17] P.M.H. Wilson: The arithmetic plurigenera of surfaces. Math. Proc. Camb. Phil. Soc.85 (1979) 25-31. Zbl0377.14007MR510396
  18. [18] P.M.H. Wilson: On complex algebraic varieties of general type; to appear in: Proceedings of conference on Algebraic Geometry, Rome1979. Symposia Math.XXIV. Zbl0462.14010MR619240
  19. [19] 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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