Abstract
Let $(X, L)$ denote a quasi-polarized manifold of dimension $n \geq 5$ defined over the field of complex numbers such that the canonical line bundle $K_{X}$ of $X$ is numerically equivalent to zero. In this paper, we consider the dimension of the global sections of $K_{X} + mL$ in this case, and we prove that $h^{0}(K_{X} + mL) > 0$ for every positive integer $m$ with $m \geq n - 3$. In particular, a Beltrametti–Sommese conjecture is true for quasi-polarized manifolds with numerically trivial canonical divisors.
Funding Statement
This research was supported by JSPS KAKENHI Grant Number 16K05103.
Citation
Yoshiaki FUKUMA. "On the positivity of the dimension of the global sections of adjoint bundle for quasi-polarized manifold with numerically trivial canonical bundle." J. Math. Soc. Japan 74 (2) 395 - 402, April, 2022. https://doi.org/10.2969/jmsj/84588458
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