Double Enneper of genus k/藤森祥一

	藤森祥一 (Shoichi Fujimori) 広島大学大学院先進理工系科学研究科数学プログラム (理学部数学科幾何学グループ)

Double Enneper of genus $k$

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$k=2$ ,

$a=-0.1$ ,

$b\approx 0.288741$ .

Weierstrass Data

$\overline{M}=\big\{(z,w)\in(\mathbb{C}\cup\{\infty\})^2\;;\;w^{k+1}=z^k(z-b)(1-bz)^k\big\},$ where $k$ is positive integer and $a$ , $b$ are constant so that $-1 < -a < 0 < b < 1$ . $M=\overline{M}\setminus\{(0,0),\,(\infty ,\infty)\},$ $g=\frac{(az-1)w}{(z-a)(z-b)},\qquad \eta = \frac{(z-a)^2(z-b)}{z^2w}dz.$ For given $k$ and $a$ , we can choose $b$ so that $f$ is single valued on $M$ .

藤森 祥一 (Shoichi Fujimori)

Double Enneper of genus kk

Weierstrass Data

藤森祥一 (Shoichi Fujimori)

Double Enneper of genus $k$