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December 2017 Second Sectional Classes of Polarized Three-folds
Yoshiaki FUKUMA
Tokyo J. Math. 40(2): 481-494 (December 2017). DOI: 10.3836/tjm/1502179238

Abstract

Let $X$ be a smooth complex projective variety of dimension $3$ and $L$ an ample line bundle on $X$. In this paper we study the second sectional class $\mathrm{cl}_{2}(X,L)$ of $(X,L)$. First we show the inequality $\mathrm{cl}_{2}(X,L)\geq L^{3}-1$, and we characterize $(X,L)$ with $-1\leq \mathrm{cl}_{2}(X,L)-L^{3}\leq 3$. Furthermore the classification of pairs $(X,L)$ with small second sectional classes is obtained. We also classify $(X,L)$ with $2L^{3}\geq \mathrm{cl}_{2}(X,L)$.

Citation

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Yoshiaki FUKUMA. "Second Sectional Classes of Polarized Three-folds." Tokyo J. Math. 40 (2) 481 - 494, December 2017. https://doi.org/10.3836/tjm/1502179238

Information

Published: December 2017
First available in Project Euclid: 9 January 2018

zbMATH: 06855945
MathSciNet: MR3743729
Digital Object Identifier: 10.3836/tjm/1502179238

Subjects:
Primary: 14C20
Secondary: 14C17, 14J30

Rights: Copyright © 2017 Publication Committee for the Tokyo Journal of Mathematics

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Vol.40 • No. 2 • December 2017
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