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A classification of polarized manifolds by the sectional Betti number and the sectional Hodge number
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Yoshiaki Fukuma
Published/Copyright:
November 28, 2008
Abstract
Let (X, L) be a polarized manifold of dimension n defined over the field of complex numbers. Assume that L is spanned. Then, in this paper, we will classify (X, L) by the second sectional Betti number b2(X, L) and the second sectional Hodge number 
(X, L) of type (1, 1), which were defined by the author in a previous paper. Moreover, for the case where L is very ample, we will give a classification of (X, L) with b4(X, L) = h4(X, ℂ).
Key words.: Polarized manifold; ample line bundle; the i-th sectional Hodge number; the i-th sectional Betti number; the i-th sectional Euler number
Received: 2007-03-12
Revised: 2007-08-09
Published Online: 2008-11-28
Published in Print: 2008-October
© de Gruyter 2008
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Keywords for this article
Polarized manifold;
ample line bundle;
the i-th sectional Hodge number;
the i-th sectional Betti number;
the i-th sectional Euler number
Articles in the same Issue
- Homogeneous geodesics of non-unimodular Lorentzian Lie groups and naturally reductive Lorentzian spaces in dimension three
- Finite type Monge–Ampère foliations
- The horofunction boundary of the Hilbert geometry
- Counting the hyperplane sections with fixed invariants of a plane quintic – three approaches to a classical enumerative problem
- Totally non-real divisors in linear systems on smooth real curves
- Covers of Klein surfaces
- A classification of polarized manifolds by the sectional Betti number and the sectional Hodge number
- On reduced polytopes and antipodality
