Projective toric polynomial generators in the unitary cobordism ring

According to Milnor and Novikov's classical result, the unitary cobordism ring is isomorphic to a graded polynomial ring with countably many generators: ${\Omega }_{\ast }^U\simeq Z[a_1,a_2,\dots ]$, $deg\left(a_i\right)=2i$. In this paper we solve the well-known problem of constructing geometric representatives for the $a_i$ among smooth projective toric varieties, $a_n=\left[X^n\right]$, ${\dim }_C{X}^n=n$. Our proof uses a family of equivariant modifications (birational isomorphisms) $B_k\left(X\right)\to X$ of an arbitrary complex manifold $X$ of complex dimension $n$ ($n\ge 2$, $k=0,\dots ,n-2$). The key fact is that the change of the Milnor number under these modifications depends only on the dimension $n$ and the number $k$ and does not depend on the manifold $X$ itself.

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