Projective Algebraic Geometry in Positive Characteristic

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400053
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Waseda University
• Principal Investigator: KAJI Hajime 早稲田大学, 理工学術院, 教授 (70194727)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 代数幾何学 / 射影双対 / ガウス写像 / 正標数

Outline of Final Research Achievements

I obtained a degree formula for Grassmann bundles associated to vector bundles on non-singular projective varieties, as a joint work with Tomohide TERASOMA. I wrote a joint paper with TERASOMA for the resuls, and published it in a scientific journal. I also studied the higher Gauss maps for projective varieties, and obtained a degree formula for the images of higher Gauss maps of Veronese varieties, which yields a generalization of the classical formula by Boole. I wrote a paper for the result of a continued work on the linear degeneration of tangentially degenerate curves, and published it in a scientific journal.

Free Research Field

代数幾何学