On the pluricanonical map of threefolds

of general type

Author:
Dong-Kwan Shin

Journal:
Proc. Amer. Math. Soc. **124** (1996), 3641-3646

MSC (1991):
Primary 14E05, 14J30

DOI:
https://doi.org/10.1090/S0002-9939-96-03865-8

MathSciNet review:
1389536

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a smooth minimal threefold of general type and let be an integer . Assume that the image of the pluricanonical map of is a curve. Then a simple computation shows that is necessarily or . When with a numerical condition or when , we obtain two inequalities and , where is the irregularity of and is the Euler characteristic of .

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Additional Information

**Dong-Kwan Shin**

Affiliation:
Department of Mathematics, Konkuk University, Seoul, 143–701, Korea

Email:
shindk@cs.sejong.ac.kr

DOI:
https://doi.org/10.1090/S0002-9939-96-03865-8

Keywords:
Threefold of general type,
pluricanonical map,
fiber space,
Euler characteristic

Received by editor(s):
June 12, 1995

Additional Notes:
This paper is supported by KOSEF and Dae-Yang Foundation

Communicated by:
Eric M. Friedlander

Article copyright:
© Copyright 1996
American Mathematical Society