Elliptic genus - yoshitake-hのブログ

http://www.ams.org/notices/200906/rtx090600720p.pdf
http://ncatlab.org/nlab/show/elliptic+genus

Def. A genus is a ring homomorphism from $\Omega^{SO}$ to a Q-algebra $\Lambda.$
Def. The logarithm of a genus $\varphi$ is the formal power series
$g(u)=\sum_{n=0}^\infty \frac{\varphi(\mathbb{C}P^{2n})}{2n+1}u^{2n+1}.$
Def. A genus is an elliptic genus if it vanishes on the associated projective bundles of even-rank complex vector bundles over close oriented manifolds.
Theorem A genus $\varphi:\Omega^{SO}\to\Lambda$ is an elliptic genus if and only if its logarithm $g(u)$ satisfies
$g(u)=\int_0^u\frac{dt}{\sqrt{1-2\delta t+\varepsilon t^2}}$
for some constants $\delta,\,\varepsilon\in\Lambda.$

この条件から楕円曲線が出てくるのがつくづく不思議だ．