2006 Fiscal Year Final Research Report Summary
Study of moduli of indecomposable modules and degeneration of modules
| Project/Area Number |
15340010
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | OKAYAMA UNIVERSITY |
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Principal Investigator |
YOSHINO Yuji Okayama University, Graduate School of Natural Science and Technology, Professor, 大学院自然科学研究科, 教授 (00135302)
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| Co-Investigator(Kenkyū-buntansha) |
YAMADA Hiro-fumi Okayama University, Graduate School of Natural Science and Technology, Professor, 大学院自然科学研究科, 教授 (40192794)
NAKAMURA Hiroaki Okayama University, Graduate School of Natural Science and Technology, Professor, 大学院自然科学研究科, 教授 (60217883)
HIRANO Yasuyuki Naruto University of Education, Natural Science Faculty, Professor, 教育学部, 教授 (90144732)
DOI Yukiko Okayama University, Faculty of Education, Professor, 教育学部, 教授 (50015765)
MIYAZAKI Mitsuhiro Kyoto University of Education, Faculty of Education, Associate Professor (90219767)
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| Project Period (FY) |
2003 – 2006
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| Keywords | commutative rings / Cohen-Macaulay modules / deformation and degeneration |
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| Research Abstract |
As a joint work with Osamu Iyama (Nagoya Univ.), we have defined the mutation as an action of braid group on the set of indecomposable objects in a general triangulated category. We have developed a general theory of mutation and have applied it to the classification problem of rigid Cohen-Macaulay modules. In particular, we succeeded to describe the perfect classification of rigid Cohen-Macaulay modules over a Veronese subring of dimension 3 and of degree 3. Through this consideration of the mutation, we are able to obtain further examples as well where we can classify the rigid Cohen-Macaulay modules. Actually the study was done by considering the maximal orthogonal subcategories in the stable category of Cohen-Macaulay modules. An investigation of the similar problem in a derived category is now in progress.
We also made a study on the deformation and the degeneration of modules. And we succeeded to construct a noncommutative parameter space of the universal deformations of a module. By this, we are now able to understand well the classical obstruction theory of modules. This noncommutative deformation theory is also in progress.
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