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By mirror symmetry, the quantum connection of a weighted projective line is closely related to the localized Fourier–Laplace transform of some Gauß–Manin system. Following an article of D’Agnolo, Hien, Morando, and Sabbah, we compute the Stokes matrices for the latter at    $$\infty $$  ∞ for the cases    $${\mathbb {P}}(1,3)$$  P ( 1 , 3 ) and    $${\mathbb {P}}(2,2)$$  P ( 2 , 2 ) by purely topological methods. We compare them to the Gram matrix of the Euler–Poincaré pairing on    $$D^b(\mathrm{Coh}({\mathbb {P}}(1,3)))$$  D b ( Coh ( P ( 1 , 3 ) ) ) and    $$D^b(\mathrm{Coh}({\mathbb {P}}(2,2)))$$  D b ( Coh ( P ( 2 , 2 ) ) ) , respectively. This article is based on the doctoral thesis of the author.

Topological computation of Stokes matrices of some weighted projective lines