Buchstaber, Ochanine, Krichever, and Witten genera

TL;DR

This paper introduces a new class of formal group laws related to Buchstaber's polynomials and explores their connections to various known genera, providing new examples beyond traditional elliptic genera.

Contribution

It defines a novel class of formal group laws, computes associated Hirzebruch genus values, and clarifies their relation to Ochanine, Krichever, and Witten genera.

Findings

Computed Hirzzebruch genus values on theta divisors and projective spaces

Established relations between the new class and existing genera

Provided examples not arising from traditional elliptic genera

Abstract

We introduce a new class of formal group laws whose modulus square construction yields Buchstaber's family of polynomials. This class is related to, but does not coincide with, the family of formal group laws associated with the Krichever genus. We compute the values of the corresponding Hirzebruch genus on theta divisors and complex projective spaces, describe its relation to the Ochanine, Krichever, and Witten genera, and show how this construction gives examples not arising from Hirzebruch's elliptic genera of level $n$.