Some tt* structures and their integral Stokes data

TL;DR

This paper characterizes quantum D-modules for certain Fano-type complete intersections by analyzing holomorphic data and integral Stokes data within the context of tt* structures and quantum cohomology.

Contribution

It provides a detailed analysis of holomorphic data and classifies solutions with integral Stokes data, linking them to quantum cohomology of specific algebraic varieties.

Findings

Characterization of quantum D-modules for Fano-type complete intersections

Enumeration of solutions with integral Stokes data

Connection between tt* structures and quantum cohomology

Abstract

In "Isomonodromy aspects of the tt* equations of Cecotti and Vafa I. Stokes data" (arxiv:1209.2045) we described all smooth solutions of the two-function tt*-Toda equations in terms of asymptotic data, holomorphic data, and monodromy data. In this supplementary article we focus on the holomorphic data and its interpretation in quantum cohomology, and enumerate those solutions with integral Stokes data. This leads to a characterization of quantum D-modules for certain complete intersections of Fano type in weighted projective spaces.