Rings of Coefficients of Universal Formal Groups for Elliptic Genus of Level N

TL;DR

This paper explores the algebraic structures underlying elliptic genera of specific levels by analyzing the rings of coefficients of specialized universal formal groups related to elliptic functions and Krichever functions.

Contribution

It describes the rings of coefficients of specialized universal Buchstaber formal groups corresponding to elliptic genera at levels 2 to 6, linking formal group theory with elliptic functions.

Findings

Explicit descriptions of coefficient rings for levels 2 to 6.

Connections established between formal groups and elliptic functions.

Advances in understanding the algebraic structure of elliptic genera.

Abstract

The paper is devoted to problems at the intersection of formal group theory, the theory of Hirzebruch genera, and the theory of elliptic functions. The elliptic function of level N determines the elliptic genus of level N as a Hirzebruch genus. It is known that the elliptic function of level N is a specialization of the Krichever function that determines the Krichever genus. The Krichever function is the exponential of the universal Buchstaber formal group. In this work we describe the rings of coefficients of specializations of universal Buchstaber formal groups that correspond to the elliptic genus of level N for N = 2,3,4,5, and 6.