Stokes matrices for the quantum differential equations of some Fano varieties

TL;DR

This paper computes the Stokes matrices for quantum differential equations of certain Fano varieties, confirming Dubrovin's conjecture for projective spaces and providing explicit formulas for hypersurfaces and weighted projective spaces.

Contribution

It introduces a method using multisummation and monodromy identity to explicitly determine Stokes matrices for various Fano varieties, extending previous results.

Findings

Confirmed Dubrovin's conjecture for projective spaces

Derived explicit formulas for Fano hypersurfaces

Extended computations to weighted projective spaces

Abstract

The classical Stokes matrices for the quantum differential equation of projective n-space are computed, using multisummation and the so-called monodromy identity. Thus, we recover the results of D. Guzzetti that confirm Dubrovin's conjecture for projective spaces. The same method yields explicit formulas for the Stokes matrices of the quantum differential equations of smooth Fano hypersurfaces in projective n-space and for weighted projective spaces.