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Pré-Publication, Document De Travail Année : 2024

Fay Identities of Pfaffian Type for Hyperelliptic Curves

Résumé

We establish identities of Pfaffian type for the theta function associated with twice or half the period matrix of a hyperelliptic curve. They are implied by the large size asymptotic analysis of exact Pfaffian identities for expectation values of ratios of characteristic polynomials in ensembles of orthogonal or quaternionic self-dual random matrices. We show that they amount to identities for the theta function with the period matrix of a hyperelliptic curve, and in this form we reprove them by direct geometric methods.
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Dates et versions

hal-04411654 , version 1 (23-01-2024)

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Gaëtan Borot, Thomas Buc-d'Alché. Fay Identities of Pfaffian Type for Hyperelliptic Curves. 2024. ⟨hal-04411654⟩
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