Microlocal analysis of constructible functions and their applications to singularity theory

• Project/Area Number: 20840040
• Research Category: Grant-in-Aid for Young Scientists (Start-up)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Kinki University
• Principal Investigator: MATSUI Yutaka Kinki University, 理工学部, 講師 (10510026)
• Project Period (FY): 2008 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥2,626,000 (Direct Cost: ¥2,020,000、Indirect Cost: ¥606,000); Fiscal Year 2009: ¥1,248,000 (Direct Cost: ¥960,000、Indirect Cost: ¥288,000); Fiscal Year 2008: ¥1,378,000 (Direct Cost: ¥1,060,000、Indirect Cost: ¥318,000)
• Keywords: 構成可能関数 / 近傍サイクル関手 / ミルナーファイバー / モノドロミーゼータ関数 / 構成可能層

Research Abstract

We studied monodromy zeta functions of Milnor fibers of Varchenko type and Jordan normal forms of monodromy of Milnor fibers by using the nearby cycle functor of constructible sheaves. For non-degenerate polynomials on affine toric varieties, we obtained similar results to classical ones. We also studied Euler obstructions of toric varieties and degree formulas for A-discriminats as applications of our results and monodromy at infinity.

Research Products

• [Journal Article] Microlocal study of Lefschetz fixed-point formulas for higher dimensional fixed point sets (2010)
  • Author(s): Yutaka MATSUI, Kiyoshi TAKEUCHI
  • Journal Title: International Mathematical Research Notices Pages: 882-913
  • Peer Reviewed
• [Journal Article] Monodromy zeta functions at infinity, Newton polyhedral and constructible sheaves (2010)
  • Author(s): Yutaka MATSUI, Kiyoshi TAKEUCHI
  • Journal Title: Mathematische Zeitschrift (出版予定)
  • Peer Reviewed
• [Journal Article] Microlocal Study of Lefschetz fixed-point formulas for higher dimensional fixed point sets (2010)
  • Author(s): Y.MATSUI
  • Journal Title: International Mathematics Research Notices 2010 Pages: 882-913
  • Peer Reviewed
• [Journal Article] Monodromy zeta functions at infinity, Netwon polyhedral and constructible sheaves (2010)
  • Author(s): Y.MATSUI
  • Journal Title: Mathematische Zeitschrift (出版予定)
  • Peer Reviewed
• [Journal Article] A-discriminants and Euler obstructions of toric varieties, RIMS Kokyuroku Bessatsu B10 (2008)
  • Author(s): Yutaka MATSUI, Kiyoshi TAKEUCHI
  • Journal Title: Differential Equations and Exact WKB Analysis Pages: 149-165
  • Peer Reviewed
• [Journal Article] A-discriminants and Euler obstructions of toric varieties (2008)
  • Author(s): Y. MATSUI
  • Journal Title: RIMS Kokyuroku Bessatsu B10 Differential Equations and Exact WKB Analysis Pages: 149-165
  • Peer Reviewed
• [Presentation] A-discriminants and monodromies of Milnor fibrations (2010)
  • Author(s): Yutaka MATSUI
  • Organizer: Microlocal analysis and related topics
  • Place of Presentation: 日本大学
  • Year and Date: 2010-03-01
• [Presentation] A-discriminants and monodromies of Milnor fibrations (2010)
  • Author(s): Y.MATSUI
  • Organizer: Microlocal Analysis and Related topics
  • Place of Presentation: 日本大学
  • Year and Date: 2010-03-01
• [Presentation] A-discriminants, GKZ hypergeometric functions and monodromy zeta functions of Milnor fibrations (2009)
  • Author(s): Yutaka MATSUI
  • Organizer: 微分方程式のモノドロミーをめぐる諸問題
  • Place of Presentation: 京都大学
  • Year and Date: 2009-02-05
• [Presentation] Topological Radon transforms and their applications to A-discriminants, Geometry and analysis on complex algebraic varieties (2008)
  • Author(s): Yutaka MATSUI
  • Organizer: Independent university of Moscow
  • Place of Presentation: Russia
  • Year and Date: 2008-09-24