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Weak boundedness theorems for canonically fibered Gorenstein minimal 3-folds

Author: Meng Chen
Journal: Proc. Amer. Math. Soc. 133 (2005), 1291-1298
MSC (2000): Primary 14C20, 14E35
Published electronically: October 18, 2004
MathSciNet review: 2111934
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Abstract: Let $X$ be a Gorenstein minimal projective 3-fold with at worst locally factorial terminal singularities. Suppose the canonical map is of fiber type. Denote by $F$ a smooth model of a generic irreducible element in fibers of $\phi_1$, and so $F$ is a curve or a smooth surface. The main result is that there is a computable constant $K$ independent of $X$ such that $g(F)\le 647$ or $p_g(F)\le 38$ whenever $p_g(X)\ge K$.

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Additional Information

Meng Chen
Affiliation: Institute of Mathematics, Fudan University, Shanghai, 200433, People’s Republic of China

Received by editor(s): September 26, 2002
Received by editor(s) in revised form: January 8, 2004
Published electronically: October 18, 2004
Additional Notes: This paper was supported by the National Natural Science Foundation of China (No.10131010), Shanghai Scientific $&$ Technical Commission (Grant 01QA14042) and SRF for ROCS, SEM
Communicated by: Michael Stillman
Article copyright: © Copyright 2004 American Mathematical Society

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