On sectional genus of quasi-polarized 3-folds

Author:
Yoshiaki Fukuma

Journal:
Trans. Amer. Math. Soc. **351** (1999), 363-377

MSC (1991):
Primary 14C20; Secondary 14J99

DOI:
https://doi.org/10.1090/S0002-9947-99-02235-7

MathSciNet review:
1487615

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Abstract: Let be a smooth projective variety over and a nef-big (resp. ample) divisor on . Then is called a quasi-polarized (resp. polarized) manifold. Then we conjecture that , where is the sectional genus of and is the irregularity of . In general it is unknown whether this conjecture is true or not, even in the case of . For example, this conjecture is true if and . But it is unknown if and . In this paper, we prove if and . Furthermore we classify polarized manifolds with , , and .

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Additional Information

**Yoshiaki Fukuma**

Affiliation:
Department of Mathematics, Faculty of Science, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152, Japan

Address at time of publication:
Department of Mathematics, College of Education, Naruto University of Education, Takashima, Naruto-cho, Naruto-shi 772-8502, Japan

Email:
fukuma@naruto-u.ac.jp

DOI:
https://doi.org/10.1090/S0002-9947-99-02235-7

Received by editor(s):
February 5, 1997

Article copyright:
© Copyright 1999
American Mathematical Society