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.
J. Math. Soc. Japan
74(2):
395-402
(April, 2022).
DOI: 10.2969/jmsj/84588458
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