클라인 4차곡선의 주기 행렬

개요

• 클라인의 4차곡선

\[x^3y+y^3z+z^3x=0\]

• \(g=3\)인 복소대수곡선
• 주기 행렬은 다음과 같이 주어진다

\[ \frac{1}{2} \left( \begin{array}{ccc} \rho & 1 & 1 \\ 1 & \rho & 1 \\ 1 & 1 & \rho \\ \end{array} \right) \] 여기서 \(\rho=\frac{-1+\sqrt{-7}}{2}\).

매스매티카 파일 및 계산 리소스

• https://docs.google.com/file/d/0B8XXo8Tve1cxN0oxOWNDdGR1eVk/edit

관련논문

• Braden, H. W., and T. P. Northover. 2010. “Klein’s Curve.” Journal of Physics A: Mathematical and Theoretical 43 (43) (October 29): 434009. doi:http://dx.doi.org/10.1088/1751-8113/43/43/434009. http://arxiv.org/abs/0905.4202.
• Tadokoro, Yuuki. 2008. “A Nontrivial Algebraic Cycle in the Jacobian Variety of the Klein Quartic.” Mathematische Zeitschrift 260 (2) (October 1): 265–275. doi:http://dx.doi.org//10.1007/s00209-007-0273-6.
• Tretkoff, C. L., and M. D. Tretkoff. 1984. “Combinatorial Group Theory, Riemann Surfaces and Differential Equations.” In Contributions to Group Theory, 33:467–519. Contemp. Math. Providence, RI: Amer. Math. Soc. http://www.ams.org/mathscinet-getitem?mr=767125.