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June 2011 A study on the dimension of global sections of adjoint bundles for polarized manifolds, II
Yoshiaki FUKUMA
Hokkaido Math. J. 40(2): 251-277 (June 2011). DOI: 10.14492/hokmj/1310042831

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 $A_{i}(X,L)$.

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Yoshiaki FUKUMA. "A study on the dimension of global sections of adjoint bundles for polarized manifolds, II." Hokkaido Math. J. 40 (2) 251 - 277, June 2011. https://doi.org/10.14492/hokmj/1310042831

Information

Published: June 2011
First available in Project Euclid: 7 July 2011

zbMATH: 1225.14007
MathSciNet: MR2840109
Digital Object Identifier: 10.14492/hokmj/1310042831

Subjects:
Primary: 14C20
Secondary: 14C17, 14J30, 14J35, 14J40

Rights: Copyright © 2011 Hokkaido University, Department of Mathematics

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Vol.40 • No. 2 • June 2011
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