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 Trudy Mat. Inst. Steklova, 2014, Volume 286, Pages 347–367 (Mi tm3568)

Smooth projective toric variety representatives in complex cobordism

Andrew Wilfong

Department of Mathematics, Eastern Michigan University, Ypsilanti, MI 48197, USA

Abstract: A general problem in complex cobordism theory is to find useful representatives for cobordism classes. One particularly convenient class of complex manifolds consists of smooth projective toric varieties. The bijective correspondence between these varieties and smooth polytopes allows us to examine which complex cobordism classes contain a smooth projective toric variety by studying the combinatorics of polytopes. These combinatorial properties determine obstructions to a complex cobordism class containing a smooth projective toric variety. However, the obstructions are only necessary conditions, and the actual distribution of smooth projective toric varieties in complex cobordism appears to be quite complicated. The techniques used here provide descriptions of smooth projective toric varieties in low-dimensional cobordism.

DOI: https://doi.org/10.1134/S0371968514030194

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English version:
Proceedings of the Steklov Institute of Mathematics, 2014, 286, 324–344

Bibliographic databases:

UDC: 515.142.426
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Citation: Andrew Wilfong, “Smooth projective toric variety representatives in complex cobordism”, Algebraic topology, convex polytopes, and related topics, Collected papers. Dedicated to Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences, on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 286, MAIK Nauka/Interperiodica, Moscow, 2014, 347–367; Proc. Steklov Inst. Math., 286 (2014), 324–344

Citation in format AMSBIB
\Bibitem{Wil14} \by Andrew~Wilfong \paper Smooth projective toric variety representatives in complex cobordism \inbook Algebraic topology, convex polytopes, and related topics \bookinfo Collected papers. Dedicated to Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences, on the occasion of his 70th birthday \serial Trudy Mat. Inst. Steklova \yr 2014 \vol 286 \pages 347--367 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm3568} \crossref{https://doi.org/10.1134/S0371968514030194} \elib{https://elibrary.ru/item.asp?id=22020648} \transl \jour Proc. Steklov Inst. Math. \yr 2014 \vol 286 \pages 324--344 \crossref{https://doi.org/10.1134/S0081543814060194} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000343605900019} \elib{https://elibrary.ru/item.asp?id=24702368} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84919799105} 

• http://mi.mathnet.ru/eng/tm3568
• https://doi.org/10.1134/S0371968514030194
• http://mi.mathnet.ru/eng/tm/v286/p347

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This publication is cited in the following articles:
1. G. D. Solomadin, Yu. M. Ustinovskiy, “Projective toric polynomial generators in the unitary cobordism ring”, Sb. Math., 207:11 (2016), 1601–1624
2. I. Yu. Limonchenko, T. E. Panov, G. Chernykh, “$SU$-bordism: structure results and geometric representatives”, Russian Math. Surveys, 74:3 (2019), 461–524
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