2011 Fiscal Year Final Research Report
Hurwitz' problem on Weierstrass points on algebraic curves
| Project/Area Number |
21540052
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| 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)
|
|---|
| Project Period (FY) |
2009 – 2011
|
| Keywords | 非特異代数曲線 / ワイエルシュトラス点 / ワイエルシュトラス半群 / 二重被覆 / 有理線織面 / 平面代数曲線 / 数値半群 |
|---|
| Research Abstract |
We are interested in Hurwitz' Problem which is the following : Find a necessary and sufficient computable condition on a numerical semigroup to be attained by a pointed curve, i. e., to be Weierstrass. This problem is not solved yet. But we got the following results : (1) Not every numerical semigroup whose minimum integer is eight(resp. twelve) is Weierstrass. (2) For a numerical semigroup H we denote by d(H) the numerical semigroup consisting of h/2 for even integer h in H. If the genus of d(H) is either 3 or 4 and the genus of H is larger than or equal to three times the genus of d(H), then H is Weierstrass. (3) We showed the following : If the genus of d(H) is larger than or equal to 5, the statement like(2) does not hold.
|
