arXiv subjects

Chikashi Miyazaki

Publications and source records attributed to Chikashi Miyazaki.

5 recordsLinked to original sources

arXiv2026

Syzygy Theoretic Approach to Horrocks-type Criteria for Vector Bundles

This paper studies a variant of Horrocks-type criteria for vector bundles mainly through a syzygy theoretic approach. Starting with sketching splitting criteria for ACM and Buchsbaum bundles on projective space, we try to give new sights of an investigation of quasi-Buchsbaum bundles. Not only our result characterizes the null-correlation bundle on P^n, but also classifies vector bundles on P^3 with simple intermediate cohomologies in terms of standard system of parameters and the corresponding skew-symmetric matrices. Our approach leads to an extended study of quasi-Buchsbaum bundles on P^n with small intermediate cohomologies.

math.AG↗

arXiv2018

Cohomological Property of Vector Bundles on Biprojective Spaces

This paper investigates the cohomological property of vector bundles on biprojective space. We will give a criterion for a vector bundle to be isomorphic to the tensor product of pullbacks of exterior products of differential sheaves.

math.AG↗

arXiv1998

Generic hyperplane section of curves and an application to regularity bounds in positive characteristic

This paper investigates the Castelnuovo-Mumford regularity of the generic hyperplane section of projective curves in positive characteristic case, and yields an application to a sharp bound on the regularity for nondegenerate projective varieties.

math.AG↗

arXiv1996

Bounds on cohomology and Castelnuovo-Mumford regularity

The Castelnuovo-Mumford regularity reg(X) of a projective scheme X was introduced by Mumford by generalizing ideas of Castelnuovo. The interest in this concept stems partly from the fact that X is m-regular if and only if for every p \geq 0 the minimal generators of the p-th syzygy module of the defining ideal I of X occur in degree \leq m + p. There are some bounds in the case that X is a locally Cohen-Macaulay scheme. The aim of this paper is to extend and improve these results for so-called (k,r)-Buchsbaum schemes. In order to prove our theorems, we need to apply a spectral sequence. We conclude by describing two sharp examples and open problems.

alg-geom↗

arXiv1996

Towards a theory of arithmetic degrees

The aim of this paper is to start a systematic investigation of the arithmetic degree of projective schemes as introduced by D. Bayer and D. Mumford. One main theme concerns itself with the behaviour of this arithmetic degree under hypersurface sections. The notion of arithmetic degree involves the new concept of length-multiplicity of embedded primary ideals. Therefore it is much harder to control the arithmetic degree under a hypersurface section than in the case for the classical degree theory. Nevertheless it has important and interesting applications. We describe such applications to the Castelnuovo-Mumford regularity and to Bezout-type theorems.

alg-geom↗