On the quantum cohomology of blow-ups of four-dimensional quadrics

TL;DR

This paper investigates the quantum cohomology of blow-ups of four-dimensional quadrics, proposing a conjecture related to Galkin's lower bound and verifying it for specific blow-up cases.

Contribution

It introduces a new conjecture in quantum cohomology and confirms its validity for certain blow-ups of four-dimensional quadrics, also establishing Conjecture $ ext{O}$ in these cases.

Findings

Conjecture related to Galkin's lower bound verified for specific blow-ups.

Conjecture $ ext{O}$ holds for these blow-up cases.

Provides evidence supporting the conjecture in higher-dimensional cases.

Abstract

We propose a conjecture relevant to Galkin's lower bound conjecture, and verify it for the blow-ups of a four-dimensional quadric at a point or along a projective plane. We also show that Conjecture $\mathcal{O}$ holds in these two cases.