Unique toric structure on a Fano Bott manifold

TL;DR

This paper proves that Fano Bott manifolds with isomorphic integral cohomology rings are actually isomorphic as toric varieties, confirming the uniqueness of their toric structure.

Contribution

It establishes the equivalence between cohomology ring isomorphisms and toric variety isomorphisms for Fano Bott manifolds, answering McDuff's question.

Findings

Cohomology ring isomorphism implies toric variety isomorphism for Fano Bott manifolds

Affirmative answer to the uniqueness of toric structure on Fano Bott manifolds

Provides a classification criterion based on cohomology rings

Abstract

We prove that if there exists a $c_1$-preserving graded ring isomorphism between integral cohomology rings of two Fano Bott manifolds, then they are isomorphic as toric varieties. As a consequence, we give an affirmative answer to McDuff's question on the uniqueness of a toric structure on a Fano Bott manifold.