## Hokkaido Mathematical Journal

### A study on the dimension of global sections of adjoint bundles for polarized manifolds, II

Yoshiaki FUKUMA

#### Abstract

Let $X$ be a smooth complex projective variety of dimension $n$ and let $L$ be an ample line bundle on $X$. In our previous paper, in order to investigate the dimension of $H^{0}(K_{X}+tL)$ more systematically, we introduced the invariant $A_{i}(X,L)$ for every integer $i$ with $0\leq i\leq n$. Main purposes of this paper are (1) to study a lower bound of $A_{i}(X,L)$ for the following two cases: (1.a) the case where $L$ is merely ample and $i\leq 3$, (1.b) the case of $h^{0}(L)>0$, and (2) to evaluate a lower bound for the dimension of $H^{0}(K_{X}+tL)$ by using $A_{i}(X,L)$.

#### Article information

Source
Hokkaido Math. J., Volume 40, Number 2 (2011), 251-277.

Dates
First available in Project Euclid: 7 July 2011

https://projecteuclid.org/euclid.hokmj/1310042831

Digital Object Identifier
doi:10.14492/hokmj/1310042831

Mathematical Reviews number (MathSciNet)
MR2840109

Zentralblatt MATH identifier
1225.14007

#### Citation

FUKUMA, Yoshiaki. A study on the dimension of global sections of adjoint bundles for polarized manifolds, II. Hokkaido Math. J. 40 (2011), no. 2, 251--277. doi:10.14492/hokmj/1310042831. https://projecteuclid.org/euclid.hokmj/1310042831