The Chern–Dold character in complex cobordisms

Let $A^{n+1} = \mathbb{C}^{n+1}/\Gamma$ be a principally polarised abelian variety. The space of holomorphic sections of its canonical line bundle $L$ is one-dimensional and generated by the classical Riemann $\theta$-function. According to the Andreotti–Mayer theorem (1967) for a generic principally polarised abelian variety, the theta divisor $\Theta^n \subset A^{n+1}$ given by the equation $\theta(z,\tau)=0$ is a smooth irreducible algebraic variety of general type.
The talk is focused on the result of V. Buchstaber and A. Veselov, obtained in 2020–2024, which is based on the construction of the Chern–Dold character in the theory of complex cobordisms (Buchstaber, 1970):
The exponential generating series of the complex cobordism classes of the theta divisors $[\Theta^n],\, n = 0,1,2,\ldots,$ realizes the exponential of the universal formal group law.
We will discuss applications of this result to well-known problems in algebraic topology and algebraic geometry, including properties of the denominators of the Todd polynomials calculated by Hirzebruch in 1956 and the hitherto open Milnor problem (1958) on Chern numbers of irreducible smooth algebraic varieties.