Pluricanonical maps for threefolds of general type

Gueorgui Tomov Todorov[1]

  • [1] University of Utah Dep. of mathematics, JWB 107 155 S 1400 E RM 233 Salt Lake City TU 84112-0090 (USA)

Annales de l’institut Fourier (2007)

  • Volume: 57, Issue: 4, page 1315-1330
  • ISSN: 0373-0956

Abstract

top
In this paper we will prove that for a threefold of general type and large volume the second plurigenera is positive and the fifth canonical map is birational.

How to cite

top

Todorov, Gueorgui Tomov. "Pluricanonical maps for threefolds of general type." Annales de l’institut Fourier 57.4 (2007): 1315-1330. <http://eudml.org/doc/10259>.

@article{Todorov2007,
abstract = {In this paper we will prove that for a threefold of general type and large volume the second plurigenera is positive and the fifth canonical map is birational.},
affiliation = {University of Utah Dep. of mathematics, JWB 107 155 S 1400 E RM 233 Salt Lake City TU 84112-0090 (USA)},
author = {Todorov, Gueorgui Tomov},
journal = {Annales de l’institut Fourier},
keywords = {Threefolds; pluricanonical maps; extension theorems; threefolds},
language = {eng},
number = {4},
pages = {1315-1330},
publisher = {Association des Annales de l’institut Fourier},
title = {Pluricanonical maps for threefolds of general type},
url = {http://eudml.org/doc/10259},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Todorov, Gueorgui Tomov
TI - Pluricanonical maps for threefolds of general type
JO - Annales de l’institut Fourier
PY - 2007
PB - Association des Annales de l’institut Fourier
VL - 57
IS - 4
SP - 1315
EP - 1330
AB - In this paper we will prove that for a threefold of general type and large volume the second plurigenera is positive and the fifth canonical map is birational.
LA - eng
KW - Threefolds; pluricanonical maps; extension theorems; threefolds
UR - http://eudml.org/doc/10259
ER -

References

top
  1. J. Chen and M. Chen and D. Zhang, The 5-canonical system on 3-folds of general type Zbl1121.14029
  2. F. Ambro, The locus of log canonical singularities Zbl1221.14004
  3. X. Benveniste, Sur les applications pluricanoniques des variété de type très général en dimension 3, Amer J. Math 108 (1986), 433-449 Zbl0601.14035MR833363
  4. E. Bombieri, Canonical models of surfaces of general type, Inst. Hautes Études Sci. Publ. 42 (1973), 171-219 Zbl0259.14005MR318163
  5. C. Hacon and J. McKernan, Boundedness of pluricanonical maps of varieties of general type Zbl1121.14011
  6. M. Chen, On pluricanonical maps for threefolds of general type, J.Math. Soc. Japan 50 (1998), 615-621 Zbl0916.14020MR1626342
  7. J. Chen and C. Hacon, Linear series of irregular varieties, (2002), World Scientific Press, Japan Zbl1094.14502MR2030451
  8. Y. Kawamata, On the extension problem of pluricanonical forms, Contemp. Math 241 (199), 193-207 Zbl0972.14005MR1718145
  9. Y. Kawamata, On Fujita’s freeness conjecture for 3-folds and 4-folds, Math. Ann. 308 (1997), 893-899 Zbl0909.14001
  10. J. McKernan, Boundedness of log terminal Fano pairs of bounded index 
  11. J. Kollár, Higher direct images of sheaves I, Ann. of Math 127 (1988), 93-163 
  12. J. Kollár, Shafarevich maps and automorphic forms, (1995), Princeton University Press, Princeton, NJ Zbl0871.14015MR1341589
  13. J. Kollár, S. Mori, Birational geometry of algebraic varieties, 134 (1998), Cambridge University Press, Cambridge Zbl0926.14003MR1658959
  14. Robert Lazarsfeld, Positivity in algebraic geometry. II, (2004), Springer-Verlag, Berlin Zbl1093.14500MR2095472
  15. S. Lee, Quint-canonical systems on canonical threefolds of index 1, Comm. Algebra 28 (2000), 5517-5530 Zbl1083.14518MR1808586
  16. S. Takayama, Pluricanonical systems on algebraic varieties of general type Zbl1108.14031
  17. H. Tsuiji, Pluricanonical systems of projective varieties of general type 

NotesEmbed ?

top

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.