Homological methods in Commutative Algebra and its applications in Geometry and Combinatorics

Project leader's name
Professor Le Tuan Hoa
Research hosting institution
Institute of Mathematics
Project duration
2016 - 2018
Scientific field(Program)
́Project’s budget
300 Mio. VND
Goal and objectives of the project

To cooperate to solve some research problems in Algebra, Geometry and Combinatorics by using homological methods and to improve research capacity and training as well as to strengthen Vitenam-Japan cooperation in the field Commutative Algebra.

Main results

Three papers supported by the project were or are accepted for the publication. Three workshops “Japan-Vietnam joint seminars on Commutative Algebra” and three schools for post-graduate students were organized. Two PhD. theses were completed during this project.

Thank to the project all 8 Vietnamese researchers (totally 11 visits) of the project visited Japan and 13 Japanese researchers visited Vietnam in order to discuss problems of interest, to give lectures or/and participate in workshops.

Novelty and actuality and scientific meaningfulness of the results

Give a solution to three problems in Commutative Algebra and deepen the Vitenam-Japan cooperation in the field Commutative Algebra.

Products of the project

- Publications: A1) Le Xuan Dung and Le Tuan Hoa, A note on Castelnuovo-Mumford regularity and Hilbert coefficients, J. Algebra and its applications, DOI: 10.1142/S02194988195019134 (đã nhận đăng) – Tạp chí SCI-E
B1) Tran Nam Trung, A classification of Gorenstein planar graphs, Advances Studies in Pure Mathematics 77, 2018; pp. 399-409 (ISBN 978-4-86497-052-5
B2) Le Tuan Hoa, Powers of Monomial Ideals and Combinatorics, arXiv:1809.07464 (nhận đăng trong Proceedings of ICAC 2017, World Scientific)
C1) S. Goto, Homological methods in Commutative Algebra, Institute of Mathematics, VAST, 2016.

- Other products: Contribute to completing two PhD. Theses
+ Ha Thi Thu Hien, “Associated prime ideals of powers of edge ideals”, defended in June 2017 (Supervisor: Prof. Ngo Viet Trung).
+ Nguyen Thi Hang, “Asymptotic behavior of some invariants of powers of cover ideals” – to be defended in 2019 (Supervisors: Tran Nam Trung and Le Thi Thanh Nhan).


The implementation of this project brings important effect on the research and training in the field Commutative Algebra at Institute of Mathematics, VAST. It also substantially deepens the research cooperation between Vietnam and Japan in this field. Therefore it would be nice if the project could be renewed in a near future.

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