Buchstaber Genus and Formal Groups

We introduce a new class of formal groups for which the modulus square construction leads to a three-parameter family of Buchstaber polynomials $B_{\mathbf{a}}(z; x, y)$ with parameters $\mathbf{a} = (a_1, a_2, a_3)$. This class is related to the family of formal groups associated with the Krichever genus, but does not coincide with it. 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 yields examples that do not arise from Hirzebruch elliptic genera of level $n$. We will discuss questions related to the construction of a generalized multiplicative complex-oriented cohomology theory $\mathrm{Bc}$, for which the map of spectra $\mathrm{MU} \longrightarrow \mathrm{Bc}$ induces on coefficient rings the Buchstaber genus $\Omega_{\mathrm{U}} \longrightarrow \mathbb{Z}[1/2, a_1, a_2, a_3]$.

The talk is based on the paper; see also the preprint arXiv:2603.21118:

M. I. Kornev, “Buchstaber, Ochanine, Krichever, and Witten genera,” Journal of Geometry and Physics, Volume 226, Number 105855, (2026).