Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Degree of the canonical map of a Gorenstein 3-fold of general type

Author(s): Jin-Xing Cai
Journal: Proc. Amer. Math. Soc. 136 (2008), 1565-1574.
MSC (2000): Primary 14J30, 14E35
Posted: December 21, 2007
MathSciNet review: 2373585
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: We prove that, for a complex projective Gorenstein 3-fold $ X$ of general type with locally factorial terminal singularities, if $ p_g(X)>105411$ and the canonical map $ \phi _X$ of $ X$ is generically finite, then $ \deg \phi _X\leq 72$.


References:

[Be]
A. Beauville, L'application canonique pour les surfaces de type qénéral, Invent. Math. 55 (1979) 121-140 MR 553705 (81m:14025)

[Fu]
T. Fujita, On Kaehler fibre spaces over curves, J. Math. Soc. Japan 30 (1978) 779-794. MR 513085 (82h:32024)

[Ha]
C. Hacon, On the degree of the canonical maps of $ 3$-folds, Proc. Japan Acad. 80 Ser. A (2004) 166-167 MR 2099745 (2005f:14079)

[M]
Y. Miyaoka, The Chern classes and Kodaira dimension of a minimal variety, in Algebraic Geometry, Sendai, 1985, Adv. Stud. Pure Math. 10 North-Holland, Amsterdam, (1987) 449-476 MR 946247 (89k:14022)

[Mu-Sa]
S. Mukai, F. Sakai, Maximal subbundles of vector bundles on a curve, Manuscripta Math. 52 (1985) 251-256 MR 790801 (86k:14013)

[P]
U. Persson, Double coverings and surfaces of general type, in Algebraic geometry, LNM 687 (1978) 168-195 MR 527234 (80h:14017)

[Pe]
C. Peters, On two types of surfaces of general type with vanishing geometric genus, Invent. Math. 32 (1976) 33-47 MR 0409482 (53:13237)

[X]
G. Xiao, Algebraic surfaces with high canonical degree, Math. Ann. 274 (1986) 473-483 MR 842626 (87g:14041)

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 14J30, 14E35

Retrieve articles in all Journals with MSC (2000): 14J30, 14E35


Additional Information:

Jin-Xing Cai
Affiliation: LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, People's Republic of China
Email: jxcai@math.pku.edu.cn

DOI: 10.1090/S0002-9939-07-09254-4
PII: S 0002-9939(07)09254-4
Received by editor(s): September 13, 2006
Received by editor(s) in revised form: February 21, 2007
Posted: December 21, 2007
Communicated by: Ted Chinburg
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia