Degree of the canonical map of a Gorenstein 3-fold of general type
HTML articles powered by AMS MathViewer
- by Jin-Xing Cai PDF
- Proc. Amer. Math. Soc. 136 (2008), 1565-1574 Request permission
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
- Arnaud Beauville, L’application canonique pour les surfaces de type général, Invent. Math. 55 (1979), no. 2, 121–140 (French). MR 553705, DOI 10.1007/BF01390086
- Takao Fujita, On Kähler fiber spaces over curves, J. Math. Soc. Japan 30 (1978), no. 4, 779–794. MR 513085, DOI 10.2969/jmsj/03040779
- Christopher Derek Hacon, On the degree of the canonical maps of 3-folds, Proc. Japan Acad. Ser. A Math. Sci. 80 (2004), no. 8, 166–167. MR 2099745
- Yoichi Miyaoka, The Chern classes and Kodaira dimension of a minimal variety, Algebraic geometry, Sendai, 1985, Adv. Stud. Pure Math., vol. 10, North-Holland, Amsterdam, 1987, pp. 449–476. MR 946247, DOI 10.2969/aspm/01010449
- Shigeru Mukai and Fumio Sakai, Maximal subbundles of vector bundles on a curve, Manuscripta Math. 52 (1985), no. 1-3, 251–256. MR 790801, DOI 10.1007/BF01171494
- Ulf Persson, Double coverings and surfaces of general type, Algebraic geometry (Proc. Sympos., Univ. Tromsø, Tromsø, 1977) Lecture Notes in Math., vol. 687, Springer, Berlin, 1978, pp. 168–195. MR 527234
- C. A. M. Peters, On two types of surfaces of general type with vanishing geometric genus, Invent. Math. 32 (1976), no. 1, 33–47. MR 409482, DOI 10.1007/BF01389770
- Gang Xiao, Algebraic surfaces with high canonical degree, Math. Ann. 274 (1986), no. 3, 473–483. MR 842626, DOI 10.1007/BF01457229
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
- Received by editor(s): September 13, 2006
- Received by editor(s) in revised form: February 21, 2007
- Published electronically: December 21, 2007
- Communicated by: Ted Chinburg
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 1565-1574
- MSC (2000): Primary 14J30, 14E35
- DOI: https://doi.org/10.1090/S0002-9939-07-09254-4
- MathSciNet review: 2373585