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 (๐‘‹, ๐ฟ) denote a quasi-polarized manifold of dimension ๐‘› โ‰ฅ 5 defined over the field of complex numbers such that the canonical line bundle ๐พ๐‘‹ of ๐‘‹ is numerically equivalent to zero. In this paper, we consider the dimension of the global sections of ๐พ๐‘‹ + ๐‘š๐ฟ in this case, and we prove that โ„Ž0(๐พ๐‘‹ + ๐‘š๐ฟ) > 0 for every positive integer ๐‘š with ๐‘š โ‰ฅ ๐‘› โˆ’3. In particular, a Beltramettiโ€“Sommese conjecture is true for quasi-polarized manifolds with numerically trivial canonical divisors.

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