Topological computation of the Stokes matrices of the weighted projective line $\mathbb{P}(1,3)$

Abstract

The localized Fourier-Laplace transform of the Gauß-Manin system of $f:{\mathbb{G}}_m\to {\mathbb{A}}^1,x\mapsto x+x^{-3}$ is a ${\mathcal{D}}_{{\mathbb{G}}_m}$-module, having a regular singularity at $0$ and an irregular one at $\infty$. By mirror symmetry, it is closely related to the quantum connection of the weighted projective line $\mathbb{P}(1,3)$. Following results of A. D'Agnolo, M. Hien, G. Morando and C. Sabbah from 2017, we compute its Stokes multipliers at $\infty$ by purely topological methods. We compare it to the Gram matrix of the Euler-Poincaré pairing on $D^b(\text{Coh}(\mathbb{P}(1,3)))$.

13 pages, 7 figures

References in corpus (2)

• Geometry and analytic theory of Frobenius manifolds
• Stokes Matrices and Monodromy of the Quantum Cohomology of Projective Spaces