Chikashi Miyazaki

Profile Information

Affiliation: Professor, Faculty of Advanced Science and Technology, Kumamoto University

Degree: PhD(Feb, 1994, Waseda University)

Contact information: cmiyazakkumamoto-u.ac.jp
Other name(s) (e.g. nickname): chikashimiyazaki
J-GLOBAL ID: 200901054168562595
researchmap Member ID: 1000310958

Research Interests

Research Areas

Natural sciences / Algebra /

Research History

Apr, 2018 - Present

Professor, Faculty of Advenced Science and Technology, Kumamoto University
Apr, 2015 - Mar, 2018

Professor, Faculty of Education, Kumamoto University
Mar, 2016 - Mar, 2016

Politecnico di Torino
Apr, 2010 - Mar, 2015

Professor, Graduate School of Science and Engineering, Saga University
Oct, 2007 - Mar, 2010

Professor, Faculty of Science and Engineering, Saga University
Apr, 1999 - Sep, 2007

Associate Professor, Faculty of Science, University of the Ryukyus
Sep, 2000 - Nov, 2000

Centre de Recerca Matematica
Apr, 1996 - Mar, 1999

Associate Professor, Department of General Education, Nagano National College of Technology
Apr, 1990 - Mar, 1996

Lecturer, Department of General Education, Nagano National College of Technology
Apr, 1994 - Mar, 1995

Massey University
Apr, 1989 - Mar, 1990

Fujitsu Ltd

Education

Apr, 1984 - Mar, 1989

Department of Mathematics, Graduate School of Science and Engineerings, DC, Waseda University
Apr, 1982 - Mar, 1984

Department od Mathematics, Graduate School of Science and Engineerings, MC, Waseda University
Apr, 1978 - Mar, 1982

Department of Mathematics, School of Science and Engineerings, Waseda University

Papers

Bounds on Castelnuovo-Mumford regularity of graded modules and projective varieties

Miyazaki C

Beitr. Algebra Geom., 60(1) 57-65, Mar, 2019 Peer-reviewed
Cohomological property of vector bundles on biprojective spaces

Francesco Malaspina, Chikashi Miyazaki

Ricerche di Matematica, 67 1-6, Jan, 2018 Peer-reviewed
Buchsbaum criterion of Segre products of vector bundles on multiprojective space

Chikashi Miyazaki

JOURNAL OF ALGEBRA, 467 47-57, Dec, 2016 Peer-reviewed
Remarks on r-planes in Complete Intersections

Chikashi Miyazaki

TOKYO JOURNAL OF MATHEMATICS, 39(2) 459-467, Dec, 2016 Peer-reviewed
A COHOMOLOGICAL CRITERION FOR SPLITTING OF VECTOR BUNDLES ON MULTIPROJECTIVE SPACE

Chikashi Miyazaki

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 143(4) 1435-1440, Apr, 2015 Peer-reviewed
BUCHSBAUM VARIETIES WITH NEXT TO SHARP BOUNDS ON CASTELNUOVO-MUMFORD REGULARITY

Chikashi Miyazaki

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 139(6) 1909-1914, Jun, 2011 Peer-reviewed
Projective curves with next to sharp bounds on Castelnuovo-Mumford regularity

Chikashi Miyazaki

JOURNAL OF ALGEBRA, 315(1) 279-285, Sep, 2007 Peer-reviewed
Castelnuovo-mumford regularity and classical method of castelnuovo

Chikashi Miyazaki

Kodai Mathematical Journal, 29(2) 237-247, 2006 Peer-reviewed
Bounds on Castelnuovo-Mumford regularity for divisors on rational normal scrolls

C Miyazaki

COLLECTANEA MATHEMATICA, 56(1) 97-102, 2005 Peer-reviewed
Generic hyperplane section of curves and an application to regularity bounds in positive characteristic

E Ballico, C Miyazaki

JOURNAL OF PURE AND APPLIED ALGEBRA, 155(2-3) 93-103, Jan, 2001 Peer-reviewed
Sharp bounds on Castelnuovo-Mumford regularity

C Miyazaki

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 352(4) 1675-1686, 2000 Peer-reviewed
174

Arithmetic and geometric degrees of graded modules

Miyazaki C, Vogel W

Commutative algebra, algebraic geometry, and computational methods, eds. Eisenbud (Springer), 97-112, 1999 Peer-reviewed
Associated primes and arithmetic degrees

C Miyazaki, W Vogel, K Yanagawa

JOURNAL OF ALGEBRA, 192(1) 166-182, Jun, 1997 Peer-reviewed
Bounds on cohomology and Castelnuovo-Mumford regularity

C Miyazaki, W Vogel

JOURNAL OF ALGEBRA, 185(3) 626-642, Nov, 1996 Peer-reviewed
Towards a theory of arithmetic degrees

C Miyazaki, W Vogel

MANUSCRIPTA MATHEMATICA, 89(4) 427-438, Apr, 1996 Peer-reviewed
BOUNDS ON CASTELNUOVO-MUMFORD REGULARITY FOR GENERALIZED COHEN-MACAULAY GRADED RINGS

LT HOA, C MIYAZAKI

MATHEMATISCHE ANNALEN, 301(3) 587-598, Mar, 1995 Peer-reviewed
A new invariant of local rings

Miyazaki C, Vogel W

C. R. Math. Rep. Acad. Sci. Canada, 117-122, 1995 Peer-reviewed
125

Spectral sequence theory for generalized Cohen-Macaulay graded modules

Miyazaki C

Commutative Algebra eds. Simis, Trung, Valla (World Scientific), 164-176, 1994 Peer-reviewed
SPECTRAL SEQUENCE THEORY OF GRADED MODULES AND ITS APPLICATION TO THE BUCHSBAUM PROPERTY AND SEGRE PRODUCTS

C MIYAZAKI

JOURNAL OF PURE AND APPLIED ALGEBRA, 85(2) 143-161, Mar, 1993 Peer-reviewed
Graded Buchsbaum algebras and Segre products

Chikashi Miyazaki

Tokyo Journal of Mathematics, 12(1) 1-20, 1989 Peer-reviewed

Misc.

2

Syzygy Theoretic Approach to Horrocks-type Criteria for Vector Bundles

Chikashi Miyazaki

arXiv>math>2403.17625, 1-18, Mar, 2024 Lead authorCorresponding author
Castelnuovo-Mumford regularity of polynomial ideals and syzygy theoretic approach to vector bundles

Chikashi Miyazaki

13-23, Mar, 2024 InvitedLead authorCorresponding author
8

ベクトル束のHorrocks-type判定法へのアプローチ --- 可換環論・シジジー手法・Castelnuovo-Mumford正則量

宮崎誓

研究集会「代数幾何学とその周辺」（休暇村南阿蘇）報告集, Mar, 2024 Lead authorCorresponding author
6

Syzygy theoretic approach to Horrocks-type theorem for vector bundles through the Castelnuovo-Mumford regularity

Chikashi Miyazaki

Nov, 2023 Lead authorCorresponding author
103

Castelnuovo-Mumford正則量とシジジーに関連する話題について

宮崎誓

第66回代数学シンポジウム報告集, 114-132, Dec, 2021 InvitedLead authorCorresponding author
190

On Horrocks-type criteria for vector bundles

Chikashi Miyazaki

93-104, Feb, 2020 InvitedLead authorCorresponding author
224

射影多様体のCastelnuovo-Mumford正則量のCastelnuovo型上限について

宮崎誓

都の西北代数幾何学シンポジウム2019 報告集, 154-162, Jan, 2020 InvitedLead authorCorresponding author
139

The Castelnuovo-Mumford regularity and the Buchsbaum property of projective varieties

Chikashi Miyazaki

2016 Lead authorCorresponding author
103

Towards a classification of Buchsbaum varieties with a regularity bound of Castelnuovo-type

Chikashi Miyazaki

The 5th Japan-Vietnam Joint Seminar on Commutative Algebra, 50-55, Aug, 2010 InvitedLead authorCorresponding author
124

Projective variety with the next extremal bound on the Castelnuovo-Mumford regularity

宮崎誓

研究集会「射影多様体の幾何とその周辺」報告集, 47-61, Feb, 2010 InvitedLead authorCorresponding author
47

Regularity of Projective curves and Classical Castelnuovo's Method

Chikashi Miyazaki

代数幾何学 in 九州報告集, 29-45, Mar, 2009 Lead authorCorresponding author
109

Bounds on the Castelnuovo-Mumford regularity of projective varieties from a viewpoint of commutative algebra

Chikashi Miyazaki

Workshop on Commutative Algebra - Interaction with Algebraic Geometry, 33-41, Feb, 2007 InvitedLead authorCorresponding author
154

Castelnuovo-Mumford regularity for projective varieties I, II

Chikashi Miyazaki

第3回代数曲線シンポジウム報告集, 81-90, 2006 InvitedLead authorCorresponding author

Presentations

11

Castelnuovo-Mumford regularity of polynomial ideals and syzygy theoretic approach to vector bundles

Chikashi Miyazaki

Mar 17, 2024 Invited
ベクトル束のホロックス型判定法へのシジジー理論的アプローチ

宮崎誓

早稲田大学セミナー, Mar 11, 2024 Invited
ベクトル束のホロックス型判定法へのシジジー理論的アプローチ

宮崎誓

九大数理代数幾何学セミナー, Feb 7, 2024
Syzygy theoretic approach to Horrocks-type theorem for vector bundles through the Castelnuovo-Mumford regularity

Chikashi Miyazaki

The 44th Symposium on Commutative Algebra, Nov 24, 2023
ベクトル束のHorrocks-type判定法へのアプローチ --- 可換環論・シジジー手法・Castelnuovo-Mumford正則量

宮崎誓

研究集会「代数幾何学とその周辺の話題」（休暇村南阿蘇）, Sep 13, 2023
12

Castelnuovo-Mumford正則量とシジジーに関連する話題について（サーベイ講演）

宮崎誓

第66回代数学シンポジウム, Sep 1, 2021 Invited
On Castelnuovo-type bounds on the Castelnuovo-Mumford regularity of projective varieties

Chikashi Miyazaki

Algebraic Geometry Symposium at Waseda, Nov 29, 2019 Invited
99

On Horrocks-type Criteria for Vector Bundles

Chikashi Miyazaki

Workshop in Projective Varieties and its related topics, Nov 4, 2019 Invited
Cohomological Criteria for Vector Bundles on Multiprojective Space

宮﨑誓

Splitting, Construction and Stability of Vector Bundles and thier Applications 九州大学, Jun, 2018 Invited
Cohomological criterion of vector bundles

宮﨑誓

第5回代数幾何学研究集会宇部, Jan, 2018 Invited
Castelnuovo-Mumford regularity from the viewpoint of Koszul cohomology

宮﨑誓

Algebraic Geometry in Kumamoto, Sep, 2017
Bounds on Castelnuovo-Mumford regularity for graded modules and projective varieties

宮﨑誓

International Conference on Commutative Algebra, Discrete Geometry and Singularity Theory, Hanoi-Halong(Vietnam), Sep, 2017 Invited
多重射影空間上の代数的ベクトル束のコホモロジー的性質

宮﨑誓

農工大数学セミナー2017, Mar, 2017 Invited
Cohomological property of vector bundles on multiprojective space

宮﨑誓

第12回代数・解析・幾何セミナー, Feb, 2017 Invited
The Castelnuovo-Mumford regularity and the Buchsbaum property of projective varieties

宮﨑誓

Seminario di Geometria in Torino(Italy), Mar, 2016 Invited
The Castelnuovo-Mumford regularity and the Buchsbaum property of projective varieties

宮﨑誓

第37回可換環論シンポジウム, Nov, 2015
多重射影空間上のベクトル束のCohen-Macaulay性、Buchsbaum性、分裂判定法

宮﨑誓

農工大数学セミナー2015, Jun, 2015, 東京農工大学 Invited
A variant of Horrocks criterion for vector bundles on multiprojective space

宮﨑誓

RIMS 研究集会, Dec, 2013 Invited
Cohomological criterion for vector bundles

宮﨑誓

Workshop on Projective Varieties, Feb, 2012
Regularity of Buchsbaum varieties

宮﨑誓

特異点とそのひろがり, Aug, 2011 Invited

Professional Memberships

Research Projects

Syzygies of Projective Varieties and Splitting of Algebraic Vector Bundles

Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, Apr, 2021 - Mar, 2026
Stanley-Reisner イデアルの算術階数とその記号的べきの射影次元

科学研究費助成事業, 基盤研究(C), 日本学術振興会, Apr, 2018 - Mar, 2023

寺井直樹, 木村杏子, 吉田健一, 宮崎誓
Castelnuovo-Mumford regularity and syzygies for projective varieties and its related topics

Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, Apr, 2014 - Mar, 2020

Miyazaki Chikashi
Arithmetical rank of Stanley-Reisner ideals and projective dimension of their powers

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, Apr, 2014 - Mar, 2017

Terai Naoki, YOSHIDA KENICHI, YANAGAWA KOUJI, KIMURA KYOUKO
Castelnuovo-Mumford regularity for projective variety and its related topics

Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, Apr, 2009 - Mar, 2014

MIYAZAKI Chikashi
Minimal free resolutions and the arithmetical rank of Stanley-Reisner ideals

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, 2011 - 2013

TERAI Naoki, UEHARA Tsuyoshi, ICHIKAWA Takashi, MIYAZAKI Chikashi, KAWAI Shigeo, YOSHIDA Kenichi, YANAGAWA Kouji, KIMURA Kyouko, MURAI Satoshi
Motivic structure of nilpotent completions of modular groups

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, 2011 - 2013

ICHIKAWA Takashi, UEHARA Tsuyoshi, MIYAZAKI Chikashi, TERAI Naoki, HIROSE Susumu
Study on the multiplicities and minimal free resolutions of Stanley-Reisner rings

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, 2008 - 2010

TERAI Naoki, UEHARA Tsuyoshi, ICHIKAWA Takashi, MIYAZAKI Chikashi, KAWAI Shigeo
Number Theory and its Development to Discrete Mathematics

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, 2008 - 2010

NAKAHARA Toru, UEHARA Tsuyoshi, MIYAZAKI Chikashi, TERAI Naoki, KATAYAMA ShinーIchi, TAGUCHI Yuuichiro, CLAUDE Levesque, KIM HyunKuang, SYED Inayat Ali Shah
Geometry of modular varieties and congruence, P-adic theory of Siegel modular forms

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, 2008 - 2010

ICHIKAWA Takashi, NAGAOKA SHOUYU, UEHARA Tsuyoshi, MIYAZAKI Chikashi, TERAI Naoki
Castelnuovo-Mumford regularity for projective varieties

Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, Apr, 2005 - Mar, 2009

MIYAZAKI Chikashi
Free resolutions of the coordinate rings of projective varieties

Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, Apr, 2002 - Mar, 2005

MIYAZAKI Chikashi
Syzygies for the defining ideal of projective varieties

Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, Apr, 1999 - Mar, 2002

MIYAZAKI Chikashi
多項式イデアルのCastelnuovo's regularityの研究

Grants-in-Aid for Scientific Research Grant-in-Aid for Encouragement of Young Scientists (A), Grant-in-Aid for Encouragement of Young Scientists (A), Japan Society for the Promotion of Science, Apr, 1997 - Mar, 1999
Classification of homogeneous ideals in terms of the degrees of generic Grobner bases

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, 1998 - 1999

AMASAKI Mutsumi, KAGEYAMA Sanpei, ISHIBASHI Yasunori, MIYAZAKI Chikashi
次数環のCastelnuovo-Mumford regularityの研究

Grants-in-Aid for Scientific Research Grant-in-Aid for Encouragement of Young Scientists (A), Grant-in-Aid for Encouragement of Young Scientists (A), Japan Society for the Promotion of Science, Apr, 1996 - Mar, 1997
Graded ringのBuchsbaum性の研究

Grants-in-Aid for Scientific Research Grant-in-Aid for Encouragement of Young Scientists (A), Grant-in-Aid for Encouragement of Young Scientists (A), Japan Society for the Promotion of Science, Apr, 1993 - Mar, 1994

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