Geodesic
Projective toric polynomial generators in the unitary cobordism ring
Sbornik. Mathematics, Tome 207 (2016) no. 11, pp. 1601-1624 Cet article a éte moissonné depuis la source Math-Net.Ru

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According to Milnor and Novikov's classical result, the unitary cobordism ring is isomorphic to a graded polynomial ring with countably many generators: $\Omega^U_*\simeq \mathbb{Z}[a_1,a_2,\dots]$, $\deg(a_i)=2i$. In this paper we solve the well-known problem of constructing geometric representatives for the $a_i$ among smooth projective toric varieties, $a_n=[X^{n}]$, $\dim_\mathbb{C} X^{n}=n$. Our proof uses a family of equivariant modifications (birational isomorphisms) $B_k(X)\to X$ of an arbitrary complex manifold $X$ of complex dimension $n$ ($n\geqslant 2$, $k=0,\dots,n-2$). 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. Bibliography: 22 titles.
Keywords: unitary cobordism, toric varieties, blow-ups, convex polytopes. 
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G. D. Solomadin; Yu. M. Ustinovskiy. Projective toric polynomial generators in the unitary cobordism ring. Sbornik. Mathematics, Tome 207 (2016) no. 11, pp. 1601-1624. http://geodesic.mathdoc.fr/item/SM_2016_207_11_a6/

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