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Stanley-Reisner イデアルの算術階数とその記号的べきの射影次元

斯坦利-赖斯纳理想的算术顺序及其象征力的投影维度

基本信息

批准号：
18K03244
负责人：
寺井直樹
金额：
$ 2.91万
依托单位：
Okayama University (2019-2022)Saga University (2018)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2018
资助国家：
日本
起止时间：
2018-04-01 至 2024-03-31
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-18K03244/
关键词：
edge ideal very well-covered projective dimension regularity edge-weighted Cohen-Macaulay unmixed Stanley-Reisner ideal second symbolic power binomial edge ideal licci second power Stanley-Reisner イデアル Gorenstein

项目摘要

可換環の極小自由分解の重要な不変量として射影次元やCastelnuovo-Mumford正則度があり、これらの探求は重要な研究課題である。２０２２年度発表の研究においては強良被覆グラフの辺イデアルに対してこれらの不変量を局所ホモロジーを用いて分析した。(K.Kimura, M.R Pournaki, N, Terai, N., S.Yassemi: Very well-covered graphs and local cohomology of their residue rings by the edge ideals. Journal of Algebra 606(2022)1-18)。エッジイデアルの高さが丁度、不定元の個数の半分である良被覆グラフは強良被覆グラフと呼ばれている。結果としてM. Mahmoudi, A. Mousivand, M. Crupi, G. Rinaldo, N. Terai, S. Yassemi, Vertex decomposability and regularity of very well-covered graphs, J. Pure Appl. Algebra 215 (10) (2011) 2473-2480.で与えたCastelnuovo-Mumford正則度を強良被覆グラフのグラフ論的不変量で表す公式やK. Kimura, N. Terai, S. Yassemi, The projective dimension of the edge ideal of a very well-covered graph, Nagoya Math. J. 230 (2018) 160-179.で与えた射影次元強良被覆グラフのグラフ論的不変量で表す公式と異なる新たな公式を与えた。

It is possible to make a small amount of free decomposition of important factors, such as projective dimensions, Castelnuovo-Mumford positivity, and exploration of important research problems. In the year 2022, the list of studies was completed and analyzed by the Bureau. (K.Kimura, M.R Pournaki, N, Terai, N., S.Yassemi: Very well-covered graphs and local cohomology of their residue rings by the edge ideals. Journal of Algebra 606 (2022) 1-18). The number of indefinite elements is very high, and the number of uncertain elements is very high. The number of uncertain elements is very high, and the number of indefinite elements is very high. Results the results showed that M. Mahmoudi, A. Mousivand, M. Crupi, G. Rinaldo, N. Terai, S. Yassemi, Vertex decomposability and regularity of very well-covered graphs, J. Pure Appl. Algebra 215 (10) (2011) 2473-2480. Kimura, N. Terai, S. Yassemi, The projective dimension of the edge ideal of a very well-covered graph, Nagoya Math. J. 230 (2018) 160179. The relationship between the projective dimension and the projective dimension is strongly influenced by the quantity table formula and the new formula.