| Project/Area Number |
19340007
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Tokyo Metropolitan University (2010)
Yokkaichi University (2009)
Kyoto University (2007-2008) |
|---|
Principal Investigator |
UENO Kenji 首都大学東京, 大学院・理工学研究科, 研究員 (40011655)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
TOKUNAGA Hiroo 首都大学東京, 大学院・理工学研究科, 教授 (30211395)
KATO Tsuyoshi 京都大学, 大学院・理学研究科, 教授 (20273427)
KATO Fumiharu 京都大学, 大学院・理学研究科, 准教授 (50294880)
SHIMIZU Yuji 国際基督教大学, 教養学部, 教授 (80187468)
望月 新一 京都大学, 数理解析研究所, 教授 (10243106)
三輪 哲二 京都大学, 大学院・理学研究科, 教授 (10027386)
井上 義也 京都大学, 大学院・理学研究科, 助教 (10232571)
|
|---|
| Project Period (FY) |
2007 – 2010
|
| Project Status |
Completed (Fiscal Year 2010)
|
| Budget Amount *help |
¥18,200,000 (Direct Cost: ¥14,000,000、Indirect Cost: ¥4,200,000)
Fiscal Year 2010: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2009: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2008: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2007: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
|
|---|
| Keywords | 代数科学 / 共形場理論 / モジュラー函手 / 位相的場の理論 / タイヒミュラー / GNS構成法 / ゲージ対称性 / 分岐被覆 / 剛幾何学 / モジュライ空 / 無限可積分系 / 代数多様体の退化 / 重複ファイバー / トロピカル幾何学 / 変形パラメータ / 導来圏 / モジュライ空間 / 接続 / ゲージ理論 / 代数曲線 / 退化 / ユニタリ性 / 写像類群 / 射影的平坦接続 / Hitchin接続 / p進剛幾何学 / ペンローズ変換 |
|---|
| Research Abstract |
From conformal field theory with gauge symmetry constructed by Tsuchiya, Yamada and Ueno I and Joergen E. Andersen constructed modular functors so that we had topological filed theory for three manifolds. When the Lie algebra for gauge symmetry is sl(n, C) we proved that our topological field is isomorphic to the one constructed by Reshetikhin and Turaev by using GNS construction of representations of Hecke algebra. As a corollary to our proof we could also prove that conformal block bundles on the Teichmueller space of pointed Riemann surfaces of genus 0 carry unitary structure compatible with KZ connections.
Ueno also constructed a family of curves over a field of characteristic p, which contain multiple fiber pD where D is any divisor appearing a degeneration of a family of curves of genus 2 and p is any prime number.
|
