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Tuesday Seminar on Topology
Seminar information archive ～04/25｜Next seminar｜Future seminars 04/26～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2021/10/19
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Yoshihiko Shinomiya (Shizuoka University)
Period matrices of some hyperelliptic Riemann surfaces (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Yoshihiko Shinomiya (Shizuoka University)
Period matrices of some hyperelliptic Riemann surfaces (JAPANESE)
[ Abstract ]
In this talk, we give new examples of period matrices of hyperelliptic Riemann surfaces. For generic genus, there were few examples of period matrices. The period matrix of a Riemann surface depends only on the choice of symplectic basis of the first homology group. It is difficult to find a symplectic basis in general. We construct hyperelliptic Riemann surfaces of generic genus from some rectangles and find their symplectic bases. Moreover, we give their algebraic equations. The algebraic equations are of the form $w^2=z(z^2-1)(z^2-a_1^2)(z^2-a_2^2) \cdots (z^2-a_{g-1}^2)$ ($1 < a_1< a_2< \cdots < a_{g-1}$). From them, we can calculate period matrices of our Riemann surfaces. We also show that all algebraic curves of this types of equations are obtained by our construction.
[ Reference URL ]In this talk, we give new examples of period matrices of hyperelliptic Riemann surfaces. For generic genus, there were few examples of period matrices. The period matrix of a Riemann surface depends only on the choice of symplectic basis of the first homology group. It is difficult to find a symplectic basis in general. We construct hyperelliptic Riemann surfaces of generic genus from some rectangles and find their symplectic bases. Moreover, we give their algebraic equations. The algebraic equations are of the form $w^2=z(z^2-1)(z^2-a_1^2)(z^2-a_2^2) \cdots (z^2-a_{g-1}^2)$ ($1 < a_1< a_2< \cdots < a_{g-1}$). From them, we can calculate period matrices of our Riemann surfaces. We also show that all algebraic curves of this types of equations are obtained by our construction.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
