The geometry of higher Weierstrass points and moduli spaces of plane algebraic curves

2014 Fiscal Year Final Research Report

• Project/Area Number: 23540041
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Saitama University
• Principal Investigator: SAKAI Fumio 埼玉大学, 理工学研究科, 教授 (40036596)
• Research Collaborator: KAWASAKI Masumi 海城高等学校, 教諭 ; WANGYU Nan 瀋陽師範大学, 講師 ; FARAHAT Mohamed Al-Azhar University, 講師
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 代数幾何 / 平面代数曲線 / 特異点 / ワイエルシュトラス点 / ゴナリティ

Outline of Final Research Achievements

We studied 3-Weierstrass points on genus two curves with extra involutions. We obtained new criterion for the gonality of singular plane curves. In particular, in case the maximal multiplicity of the singular points is equal to three, we obtained the almost optimal criterion. We introduced a new invariant V defined by the multiplicities of singular points. We also considered the lower bound of the gonality. We classified hyperelliptic curves among cyclic coverings of the projective line. We published papers on these topics.

Free Research Field

数物系科学 B