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

This article is cited in 2 scientific papers (total in 2 papers)

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
Received in December 2013
Language:

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, Tr. Mat. Inst. Steklova, 286, MAIK Nauka/Interperiodica, Moscow, 2014, 347–367; Proc. Steklov Inst. Math., 286 (2014), 324–344

Citation in format AMSBIB
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\bookinfo Collected papers. Dedicated to Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences, on the occasion of his 70th birthday
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\vol 286
\pages 347--367
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. I. Yu. Limonchenko, T. E. Panov, G. Chernykh, “$SU$-bordism: structure results and geometric representatives”, Russian Math. Surveys, 74:3 (2019), 461–524  mathnet  crossref  crossref  adsnasa  isi  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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