The $c_1$-cohomological rigidity conjecture for smooth toric Fano varieties

Let $X$ and $Y$ be smooth toric Fano varieties. A $c_1$-preserving graded ring isomorphism is a graded ring isomorphism between their integral cohomology rings that preserves the first Chern classes of $X$ and $Y$.

$c_1$-cohomological rigidity conjecture. If there exists a $c_1$-preserving graded ring isomorphism between the integral cohomology rings of $X$ and $Y$, then $X$ and $Y$ are isomorphic as varieties.

The paper confirms this conjecture for smooth toric Fano varieties of Picard number two; the general case remains outside the result stated here.