2022 年 74 巻 2 号 p. 395-402
Let (𝑋, 𝐿) denote a quasi-polarized manifold of dimension 𝑛 ≥ 5 defined over the field of complex numbers such that the canonical line bundle 𝐾𝑋 of 𝑋 is numerically equivalent to zero. In this paper, we consider the dimension of the global sections of 𝐾𝑋 + 𝑚𝐿 in this case, and we prove that ℎ0(𝐾𝑋 + 𝑚𝐿) > 0 for every positive integer 𝑚 with 𝑚 ≥ 𝑛 −3. In particular, a Beltrametti–Sommese conjecture is true for quasi-polarized manifolds with numerically trivial canonical divisors.
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