Some remarks on Landau-Ginzburg potentials for odd-dimensional quadrics

TL;DR

This paper investigates the construction of Frobenius manifolds for Landau-Ginzburg models of odd-dimensional quadrics and their relation to quantum cohomology, showing initial conditions can be derived from a modified model.

Contribution

It demonstrates how to modify the standard Landau-Ginzburg model to match the Frobenius manifold of quantum cohomology for odd-dimensional quadrics.

Findings

Initial conditions of quantum cohomology Frobenius manifold are obtainable from the modified Landau-Ginzburg model.

Establishes a connection between Landau-Ginzburg models and quantum cohomology for odd-dimensional quadrics.

Provides a framework for constructing Frobenius manifolds in this geometric context.

Abstract

We study the possibility of constructing a Frobenius manifold for the standard Landau-Ginzburg model of odd-dimensional quadrics $Q_{2n+1}$ and matching it with the Frobenius manifold attached to the quantum cohomology of these quadrics. Namely, we show that the initial conditions of the quantum cohomology Frobenius manifold of the quadric can be obtained from the suitably modified standard Landau-Ginzburg model.