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Tr. Mat. Inst. Steklova, 2018, Volume 302, Pages 287–295 (Mi tm3922)  

This article is cited in 1 scientific paper (total in 1 paper)

Calabi–Yau hypersurfaces and SU-bordism

Ivan Yu. Limonchenkoa, Zhi Lüa, Taras E. Panovbcd

a School of Mathematical Sciences, Fudan University, 220 Handan Road, Shanghai, 200433, P.R. China
b Institute for Theoretical and Experimental Physics named by A.I. Alikhanov of National Research Centre "Kurchatov Institute", Bol'shaya Cheremushkinskaya ul. 25, Moscow, 117218 Russia
c Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991 Russia
d Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Bol'shoi Karetnyi per. 19, str. 1, Moscow, 127051 Russia

Abstract: V. V. Batyrev constructed a family of Calabi–Yau hypersurfaces dual to the first Chern class in toric Fano varieties. Using this construction, we introduce a family of Calabi–Yau manifolds whose $\mathrm {SU}$-bordism classes generate the special unitary bordism ring $\varOmega ^{\mathrm {SU}}[\tfrac 12]\cong \mathbb {Z}[\tfrac 12][y_i\colon i\ge 2]$. We also describe explicit Calabi–Yau representatives for multiplicative generators of the $\mathrm {SU}$-bordism ring in low dimensions.

Funding Agency Grant Number
China Postdoctoral Science Foundation 2016M601486
National Natural Science Foundation of China 11371093
11661131004
11431009
Russian Foundation for Basic Research 17-01-00671
18-51-50005
Simons Foundation
The first author was supported by the General Financial Grant from the China Postdoctoral Science Foundation, grant no. 2016M601486. The second author was supported by the NSFC, grant nos. 11371093, 11661131004 and 11431009. The third author was supported by the Russian Foundation for Basic Research (project nos. 17-01-00671 and 16-51-55017) and by the Simons–IUM fellowship.


DOI: https://doi.org/10.1134/S0371968518030135

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English version:
Proceedings of the Steklov Institute of Mathematics, 2018, 302, 270–278

Bibliographic databases:

Document Type: Article
UDC: 515.14+515.16
MSC: Primary 57R77, Secondary 14M25
Received: March 15, 2018

Citation: Ivan Yu. Limonchenko, Zhi Lü, Taras E. Panov, “Calabi–Yau hypersurfaces and SU-bordism”, Topology and physics, Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 80th birthday, Tr. Mat. Inst. Steklova, 302, MAIK Nauka/Interperiodica, Moscow, 2018, 287–295; Proc. Steklov Inst. Math., 302 (2018), 270–278

Citation in format AMSBIB
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\by Ivan~Yu.~Limonchenko, Zhi~Lü, Taras~E.~Panov
\paper Calabi--Yau hypersurfaces and SU-bordism
\inbook Topology and physics
\bookinfo Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 80th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2018
\vol 302
\pages 287--295
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3922}
\crossref{https://doi.org/10.1134/S0371968518030135}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2018
\vol 302
\pages 270--278
\crossref{https://doi.org/10.1134/S0081543818060135}
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    This publication is cited in the following articles:
    1. V. M. Buchstaber, “Cobordisms, manifolds with torus action, and functional equations”, Proc. Steklov Inst. Math., 302 (2018), 48–87  mathnet  crossref  crossref  isi
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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