  We show that the smooth theta divisors of general principally polarised
abelian varieties can be chosen as irreducible algebraic representatives of the
coefficients of the Chern-Dold character in complex cobordisms and describe the
action of the Landweber-Novikov operations on them. We introduce a quantisation
of the complex cobordism theory with the dual Landweber-Novikov algebra as the
deformation parameter space and show that the Chern-Dold character can be
interpreted as the composition of quantisation and dequantisation maps. Some
smooth real-analytic representatives of the cobordism classes of theta divisors
are described in terms of the classical Weierstrass elliptic functions. The
link with the Milnor-Hirzebruch problem about possible characteristic numbers
of irreducible algebraic varieties is discussed.

Algebraic Topology;Algebraic Geometry