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

TL;DR

This paper proves the $c_1$-cohomological rigidity conjecture for smooth toric Fano varieties with Picard number two, showing that cohomology ring isomorphisms preserving $c_1$ imply isomorphism of the varieties.

Contribution

It confirms the $c_1$-cohomological rigidity conjecture specifically for smooth toric Fano varieties of Picard number two, a previously unresolved case.

Findings

The conjecture holds for Picard number two cases.

Cohomology ring isomorphisms preserving $c_1$ determine variety isomorphism.

Advances understanding of rigidity in toric Fano varieties.

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 two.