2015 Fiscal Year Annual Research Report
| Project/Area Number |
15F15751
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| Research Institution | Kyoto University |
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Principal Investigator |
向井 茂 京都大学, 数理解析研究所, 教授 (80115641)
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| Co-Investigator(Kenkyū-buntansha) |
HEDEN ISAC 京都大学, 数理解析研究所, 外国人特別研究員
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| Project Period (FY) |
2015-10-09 – 2018-03-31
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| Keywords | 代数学 |
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| Outline of Annual Research Achievements |
Heden has been studying the decomposition group of a line L in the projective plane, i.e. the subgroup of birational transformations of the plane that send L to itself birationally. This is a joint work with S. Zimmermann (Basel University), and they have been able to prove that this group is generated by its elements of degree 1 and one element of degree 2 and also that it does not decompose as a non-trivial amalgamated product. These results were submitted to a mathematical journal for publication in January and after receiving a positive report, we are now working on minor revisions. We have also started to write down some generalizations that came out of discussions when he traveled to Switzerland in January to participate in "5th Swiss-French workshop on algebraic geometry" - in particular some similar results about rational plane curves of higher degree.
At the conference “14th affine algebraic geometry meeting” in Osaka, related to his talk, a collaboration with A. Dubouloz (Bourgogne University) and T. Kishimoto (Saitama University) was initiated. Given the spectrum S of a regular 2-dimensional local ring, with closed point o, and a non-trivial principal additive bundle P over S-{o}, they try to classify all affine extensions P’ of P, i.e. affine Ga-threefolds P’ that can be obtained from P by adding a fiber over the point o. They are making progress on the problem.
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| Current Status of Research Progress |
Current Status of Research Progress
1: Research has progressed more than it was originally planned.
Reason
Heden is quite happy with the results obtained so far, they correspond roughly to the plans in his research proposal. The research environment at RIMS is outstanding, the generous research-in-aid grant has allowed me to purchase a computer and to travel to conferences and seminars, and the secretaries have been very helpful with all administration, including practical issues about living in Kyoto, so I have been able to focus fully on research.
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| Strategy for Future Research Activity |
Heden has been organising an informal reading seminar with other postdoctoral fellows at RIMS on Mori theory. They have been reading Matsuki’s book “Introduction to the Mori program”. Heden expects that this will be very useful for him as he plans to use the Sarkisov program in my study of subgroups of Bir(P^3) as described in the second half of my research plan.
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