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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2024, Volume 326, Pages 368–381
DOI: https://doi.org/10.4213/tm4395 (Mi tm4395) 		 
$c_1$-Cohomological Rigidity for Smooth Toric Fano Varieties of Picard Number Two

Yunhyung Choa, Eunjeong Leeb, Mikiya Masudac, Seonjeong Parkd

a Department of Mathematics Education, Sungkyunkwan University, Seoul 03063, Republic of Korea
b Department of Mathematics, Chungbuk National University, Cheongju 28644, Republic of Korea
c Osaka Central Advanced Mathematical Institute, Osaka Metropolitan University, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
d Department of Mathematics Education, Jeonju University, Jeonju 55069, Republic of Korea
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DOI: https://doi.org/10.4213/tm4395
Abstract: The $c_1$-cohomological rigidity conjecture states that two smooth toric Fano varieties are isomorphic as varieties if there is a $c_1$-preserving isomorphism between their integral cohomology rings. In this paper, we confirm the conjecture for smooth toric Fano varieties of Picard number $2$.
Keywords: $c_1$-cohomological rigidity, toric Fano varieties, generalized Bott manifolds
Funding agency Grant number
National Research Foundation of Korea 2020R1C1C1A01010972
2020R1A5A1016126
RS-2023-00239947
NRF-2020R1A2C1A01011045
Japan Society for the Promotion of Science 22K03292
HSE Basic Research Program
Ministry of Education, Culture, Sports, Science and Technology, Japan
Y. Cho was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP; Ministry of Science, ICT and Future Planning), nos. 2020R1C1C1A01010972 and 2020R1A5A1016126. E. Lee was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT), no. RS-2023-00239947. M. Masuda was supported in part by the JSPS Grant-in-Aid for Scientific Research 22K03292 and by the HSE University Basic Research Program. S. Park was supported by the National Research Foundation of Korea, no. NRF-2020R1A2C1A01011045. This work was also supported in part by Osaka Central Advanced Mathematical Institute (MEXT Joint Usage/Research Center on Mathematics and Theoretical Physics).
Received: September 29, 2023
Revised: January 31, 2024
Accepted: May 2, 2024
English version:
Proceedings of the Steklov Institute of Mathematics, 2024, Volume 326, Pages 339–351
DOI: https://doi.org/10.1134/S0081543824040163
Document Type: Article
Language: Russian
Citation: Yunhyung Cho, Eunjeong Lee, Mikiya Masuda, Seonjeong Park, “$c_1$-Cohomological Rigidity for Smooth Toric Fano Varieties of Picard Number Two”, Topology, Geometry, Combinatorics, and Mathematical Physics, Collected papers. Dedicated to Victor Matveevich Buchstaber on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 326, Steklov Math. Inst., Moscow, 2024, 368–381; Proc. Steklov Inst. Math., 326 (2024), 339–351
Citation in format AMSBIB
\Bibitem{ChoLeeMas24}
\by Yunhyung~Cho, Eunjeong~Lee, Mikiya~Masuda, Seonjeong~Park
\paper $c_1$-Cohomological Rigidity for Smooth Toric Fano Varieties of Picard Number Two
\inbook Topology, Geometry, Combinatorics, and Mathematical Physics
\bookinfo Collected papers. Dedicated to Victor Matveevich Buchstaber on the occasion of his 80th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2024
\vol 326
\pages 368--381
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4395}
\crossref{https://doi.org/10.4213/tm4395}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2024
\vol 326
\pages 339--351
\crossref{https://doi.org/10.1134/S0081543824040163}
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