Translator Disclaimer
April, 2021 On the positivity of the dimension of the global sections ofadjoint bundle for quasi-polarized manifold with numerically trivial canonical bundle
Yoshiaki FUKUMA
Author Affiliations +
J. Math. Soc. Japan Advance Publication 1-8 (April, 2021). DOI: 10.2969/jmsj/84588458

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

Download Citation

Yoshiaki FUKUMA. "On the positivity of the dimension of the global sections ofadjoint bundle for quasi-polarized manifold with numerically trivial canonical bundle." J. Math. Soc. Japan Advance Publication 1 - 8, April, 2021. https://doi.org/10.2969/jmsj/84588458

Information

Received: 6 April 2020; Revised: 8 September 2020; Published: April, 2021
First available in Project Euclid: 13 April 2021

Digital Object Identifier: 10.2969/jmsj/84588458

Subjects:
Primary: 14C20
Secondary: 14J40

Rights: Copyright © 2021 Mathematical Society of Japan

JOURNAL ARTICLE
8 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Advance Publication
Back to Top