On Galkin's Lower Bound Conjecture

Abstract

We estimate an upper bound of the spectral radius of a linear operator on the quantum cohomology of the toric Fano manifolds ${\mathbb{P}}_{{\mathbb{P}}^n}(\mathcal{O}\oplus \mathcal{O}(3))$. This provides a negative answer to Galkin's lower bound conjecture.

6 pages