## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### A note on the dimension of global sections of adjoint bundles for polarized 4-folds

Yoshiaki Fukuma

#### Abstract

Let $(X,L)$ be a polarized manifold defined over the field of complex numbers. In this paper, we consider the case where $\dim X=4$ and we prove that the second Hilbert coefficient $A_{2}(X,L)$ of $(X,L)$, which was defined in our previous paper, is non-negative. Furthermore we consider a question proposed by H. Tsuji for $\dim X=4$.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 94, Number 5 (2018), 53-58.

Dates
First available in Project Euclid: 27 April 2018

https://projecteuclid.org/euclid.pja/1524794416

Digital Object Identifier
doi:10.3792/pjaa.94.53

Mathematical Reviews number (MathSciNet)
MR3795748

Zentralblatt MATH identifier
1126.14009

Subjects
Primary: 14C20: Divisors, linear systems, invertible sheaves
Secondary: 14J35: $4$-folds

#### Citation

Fukuma, Yoshiaki. A note on the dimension of global sections of adjoint bundles for polarized 4-folds. Proc. Japan Acad. Ser. A Math. Sci. 94 (2018), no. 5, 53--58. doi:10.3792/pjaa.94.53. https://projecteuclid.org/euclid.pja/1524794416

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