2003 Fiscal Year Final Research Report Summary
Studis on local signature and monodromy of degenerate families of algebraic carves
| Project/Area Number |
14540039
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Tohoku-Gakuin University |
|---|
Principal Investigator |
ASHIKAGA Tadashi Tohoku-Gakuin University, Faculty of Engineering, Professor, 工学部, 教授 (90125203)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
KONNO Kazuhiro Tohoku-Gakuin University, Mathematical Institute of Graduate school of Osaka University, Professor, 大学院・理学研究科, 教授 (10186869)
TSUCHIHASHI Hiroyasu Tohoku-Gakuin University, Faculty of general Education, Associate Professor, 教養学部, 助教授 (00146119)
|
|---|
| Project Period (FY) |
2002 – 2003
|
| Keywords | Degeneration / Signature / Monodromy / Localization / Families of algebraic carves / Stable reduction / Pedeking Sum / Fixed point theorem |
|---|
| Research Abstract |
The aim to obtain an explicit formula of local signature for the contribution of semi-stable reduction coas completed by applying Atiyah-Singer's G-signature theovem, The main termof the formula consists of Pedeking sams of Nielsen-Matsumoto-Moutesions' monodromy data, and I wrote it in Kokyuroku RIMS1345(2003), PP.203-237.
The aim to compare Furuta's local signature and Yoshikawa's local signature was almost settled, and I wrote it in the previous RIMS report. But Yoshikawa critacize a cerlain part of the argument, and my study in still on the way at this point.
On the other hand, I also obtained a formula for the contribution of semi-stavle reduction to Yoshikawa's local signature by using Atiyah-Botl-Segal-Singer's fixed point formula, and I gave a lecture forit at the symposium "Algobraic Geomety and Topoloy of Hodge Theory, Degnerations and Complex Sarface", I am preparing the full paper of these results.
|
