Projective toric polynomial generators in the unitary cobordism ring

Abstract

According to Milnor and Novikov's classical result, the unitary cobordism ring is isomorphic to a graded polynomial ring with countably many generators: , . In this paper we solve the well-known problem of constructing geometric representatives for the among smooth projective toric varieties, , . Our proof uses a family of equivariant modifications (birational isomorphisms) of an arbitrary complex manifold of complex dimension (, ). The key fact is that the change of the Milnor number under these modifications depends only on the dimension and the number and does not depend on the manifold itself. Bibliography: 22 titles.