| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
We study a squarefree monomial ideal of a polynomial ring over a field. The main theme of the project is to clarify relations between the arithmetical rank of the ideal, especially a construction of elements which generate the ideal up to radical, and a free resolution of its quotient ring. We proved that the arithmetical rank is equal to the projective dimension for a Gorenstein squarefree monomial ideal of height 3 (joint work with Naoki Terai) and a squarefree monomial ideal whose associated hypergraph is a string or a cycle (joint work with Paolo Mantero).
Another theme of the project is the study of a minimal free resolution of an edge ideal. We obtain some results, for example, a new sufficient condition for the non-vanishing of the Betti numbers of an edge ideal.
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