Hurwitz' problem through double covers of curves and curves on surfaces

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540057
• 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, 基礎・教養教育センター, 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, 教授 (10211111)
• Research Collaborator: HARUI Takeshi ; WATANABE Kenta ; KAWAGUCHI Ryo ; TAKAHASHI Takeshi
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: ワイエルシュトラス半群 / 数値半群 / 代数曲線 / 二重被覆 / Ｋ３曲面 / 平面代数曲線 / 有理曲面

Outline of Final Research Achievements

A research collaboration person and I studied on the Weierstrass semigroups of ramification points on double covers of plane curves of degree 4 and three papers about this subject were published or accepted for publication. Another research collaboration person and I investigated the Weierstrass semigroups of ramification points on double covers of plane curves which can be extended to double covers of projective planes, which may have singularities (if the double covers have no singularities, then they are K3 surfaces). We submitted the paper about this topic, and the paper was accepted.
The joint work with the overseas co-investigator was publised. The title is Weierstrass semigroups on double coverings of genus 4 curves. Moreover, the co-investigator and I got the result on the Weierstrass semigroups of ramification points of double covers of plane curves of degree 5 when the genera of the double covers are larger than 17. The paper about this result is being printed at present.

Free Research Field

代数幾何学