## Hokkaido Mathematical Journal

- Hokkaido Math. J.
- Volume 42, Number 3 (2013), 463-472.

### Classification of polarized manifolds by the second sectional Betti number

#### Abstract

Let *X* be an *n*-dimensional smooth projective variety defined over the field of complex numbers, let *L* be an ample and spanned line bundle on *X*. Then we classify (*X,L*) with *b*_{2}(*X,L*) = *h*^{2}(*X*,ℂ)+1, where *b*_{2}(*X,L*) is the second sectional Betti number of (*X,L*).

#### Article information

**Source**

Hokkaido Math. J., Volume 42, Number 3 (2013), 463-472.

**Dates**

First available in Project Euclid: 12 November 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.hokmj/1384273393

**Digital Object Identifier**

doi:10.14492/hokmj/1384273393

**Mathematical Reviews number (MathSciNet)**

MR3137396

**Zentralblatt MATH identifier**

1282.14012

**Subjects**

Primary: 14C20: Divisors, linear systems, invertible sheaves

Secondary: 14C17: Intersection theory, characteristic classes, intersection multiplicities [See also 13H15] 14J30: $3$-folds [See also 32Q25] 14J35: $4$-folds 14J40: $n$-folds ($n > 4$)

**Keywords**

Polarized manifold ample line bundle adjunction theory sectional Betti number

#### Citation

Fukuma, Yoshiaki. Classification of polarized manifolds by the second sectional Betti number. Hokkaido Math. J. 42 (2013), no. 3, 463--472. doi:10.14492/hokmj/1384273393. https://projecteuclid.org/euclid.hokmj/1384273393