| 研究実績の概要 |
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.
|
| 現在までの達成度 (区分) |
現在までの達成度 (区分)
1: 当初の計画以上に進展している
理由
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.
|
