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2016 Toric polynomial generators of complex cobordism
Andrew Wilfong
Algebr. Geom. Topol. 16(3): 1473-1491 (2016). DOI: 10.2140/agt.2016.16.1473


Although it is well known that the complex cobordism ring ΩU is isomorphic to the polynomial ring [α1,α2,], an explicit description for convenient generators α1,α2, has proven to be quite elusive. The focus of the following is to construct complex cobordism polynomial generators in many dimensions using smooth projective toric varieties. These generators are very convenient objects since they are smooth connected algebraic varieties with an underlying combinatorial structure that aids in various computations. By applying certain torus-equivariant blow-ups to a special class of smooth projective toric varieties, such generators can be constructed in every complex dimension that is odd or one less than a prime power. A large amount of evidence suggests that smooth projective toric varieties can serve as polynomial generators in the remaining dimensions as well.


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Andrew Wilfong. "Toric polynomial generators of complex cobordism." Algebr. Geom. Topol. 16 (3) 1473 - 1491, 2016.


Received: 11 September 2014; Revised: 10 April 2015; Accepted: 27 October 2015; Published: 2016
First available in Project Euclid: 28 November 2017

zbMATH: 1350.57036
MathSciNet: MR3523047
Digital Object Identifier: 10.2140/agt.2016.16.1473

Primary: 14M25 , 57R77
Secondary: 52B20

Keywords: Blow-up , cobordism , fan , toric variety

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.16 • No. 3 • 2016
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