Journal of the Mathematical Society of Japan
Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645
On the positivity of the dimension of the global sections of adjoint bundle for quasi-polarized manifold with numerically trivial canonical bundle
Yoshiaki Fukuma
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2022 Volume 74 Issue 2 Pages 395-402

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Abstract

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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