Research of non-commutative geometry, singular point, and geometric asymptotics

2014 Fiscal Year Final Research Report

• Project/Area Number: 22540095
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Keio University
• Principal Investigator: MIYAZAKI Naoya 慶應義塾大学, 経済学部, 教授 (50315826)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 非可換幾何学 / シンプレクティック幾何学 / 一般複素幾何学 / 量子化 / 指数定理 / フーリエ積分作用素

Outline of Final Research Achievements

First, I introduced non-commutative deformation of structure sheaves of schemes, and I cnstructed a concrete example via complex projective spaces. Furthermore, I computed exponential map with respect to a new product. Second, with Hideki Omori, Yoshiaki Maeda, Akira Yoshioka, we studied the ordering problem on a flat space, and convergent problem with respect to a parameter h. Third, with Yasushi Homma, Tatsuya Tate, we sudy eta functions for Dirac operators on 3-manifolds (e.g. Heisenberg manifold, Lenz spaces etc.). Fourth, with Tadashi Taniguchi, we study quantization of super Calabi-Yau twistor spaces endowed with super Poisson structure via Penrose double fibration.

Free Research Field

幾何学