Study of cusp singularities by the theory of Groebner basis

2014 Fiscal Year Final Research Report

• Project/Area Number: 24654003
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Tohoku University
• Principal Investigator: ISHIDA Masanori 東北大学, 理学(系)研究科(研究院), 教授 (30124548)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 代数幾何学 / 代数多様体 / トーリック多様体 / カスプ特異点 / 鏡映群 / グレブナー基底

Outline of Final Research Achievements

We studied on toric type cusp singularities with the method of Groebner basis. In particular, we proved that cusp singularities are constructed over any field as noetherian complete local rings. We can define the leading terms ideal for an ideal of the local ring, and use it for comparing ideals similarly as the case of the polynomial ring.
In order to generalize and construct cusp singularities, we defined quasi-polyhedral sets and studied some fundamental properties and examples with the action of reflection groups.

Free Research Field

代数幾何学