On the canonical ring of algebraic varieties

P. M. H. Wilson

Compositio Mathematica (1981)

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

How to cite


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

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},

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 -


  1. [1] M.F. Atiyah: Some examples of complex manifolds. Bonn Math. Schriften6 (1958). Zbl0080.37502MR105718
  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

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.