Research on Hurwitz's problem and K3 surfaces through double covers of curves and symmetric numerical semigroups

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04830
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Kanagawa Institute of Technology
• Principal Investigator: Komeda Jiryo 神奈川工科大学, 公私立大学の部局等, 教授 (90162065)
• Co-Investigator(Renkei-kenkyūsha): OHBUCHI Akira 徳島大学, 大学院ソシオアーツアンドサイエンス研究部 (10211111)
• Research Collaborator: MATSUTANI Shigeki ; TAKAHASI Takeshi ; HARUI Takeshi ; KAWAGUCHI Ryo ; WATANABE Kenta ; MASE Makiko
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: ワイエルシュトラス半群 / ガロア・ワイエルシュトラス点 / 2重被覆 / 代数曲線の3重被覆 / 平面代数曲線 / K3曲面 / トーリック曲面 / 射影直線の巡回被覆

Outline of Final Research Achievements

A research collaboration person and I wrote the article on the conditions for Weierstrass semigroups gained from those of ramification points of double coverings, which was published. An overseas collaborator and I wrote the articles on the Weierstrass semigroups of the ramification points of double covering of plane curves of degree 6 (resp. 5) over total flexes (resp. total flexes and non-ordinary flexes), which were also published. The articles on Galois Weierstrass points (resp. Riemann constants) were published. Those papers are joint works with research collaboration people. Moreover, the other two accepted articles were published.
The three papers were published in the research reports of my university and the other three articles were published in RIMS Kokyuroku. Moreover, the number of oral presentations in workshops is 11. A research collaboration person and I organized the symposium on algebraic curves every year.

Free Research Field

代数幾何学