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The $c_1$-cohomological rigidity conjecture states that two smooth toric Fanovarieties are isomorphic as varieties if there is a $c_1$-preservingisomorphism between their integral cohomology rings. In this paper, we confirmthe conjecture for smooth toric Fano varieties of Picard number two.

$c_1$-cohomological rigidity for smooth toric Fano varieties of Picard number two