Yunhyung Cho, Eunjeong Lee, Mikiya Masuda, Seonjeong Park, “<nobr>$c_1$</nobr>-Cohomological Rigidity for Smooth Toric Fano Varieties of Picard Number Two”, Trudy Mat. Inst. Steklova, 2024, Volume 326,Pages <nobr>368

$c_1$-Cohomological Rigidity for Smooth Toric Fano Varieties of Picard Number Two

Yunhyung Cho^a, Eunjeong Lee^b, Mikiya Masuda^c, Seonjeong Park^d

^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

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.

Received: September 29, 2023
Revised: January 31, 2024
Accepted: May 2, 2024

DOI: 10.4213/tm4395