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Another algebraic proof of Weil's reciprocity

Emma Previato — 1991

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The Burchnall-Chaundy-Krichever correspondence which converts meromorphic functions on a curve into differential operators is used to interpret Weil's reciprocity as the calculation of a resultant.

Sui sottogruppi di Dedekind nei gruppi infiniti

Emma Previato — 1976

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Sei G eine Gruppe und H eine Untergruppe von G. Es wird eine hinreichende Bedingung, damit H eine modulare Untergruppe von G sei, angegeben.

Singularities of 2 Θ -divisors in the jacobian

Christian PaulyEmma Previato — 2001

Bulletin de la Société Mathématique de France

We consider the linear system | 2 Θ 0 | of second order theta functions over the Jacobian J C of a non-hyperelliptic curve C . A result by J.Fay says that a divisor D | 2 Θ 0 | contains the origin 𝒪 J C with multiplicity 4 if and only if D contains the surface C - C = { 𝒪 ( p - q ) p , q C } J C . In this paper we generalize Fay’s result and some previous work by R.C.Gunning. More precisely, we describe the relationship between divisors containing 𝒪 with multiplicity 6 , divisors containing the fourfold C 2 - C 2 = { 𝒪 ( p + q - r - s ) p , q , r , s C } , and divisors singular along C - C , using the third exterior...

Quasi-periodic and periodic solutions of the Toda lattice via the hyperelliptic sigma function

Yuji KodamaShigeki MatsutaniEmma Previato — 2013

Annales de l’institut Fourier

A lattice model with exponential interaction, was proposed and integrated by M. Toda in the 1960s; it was then extensively studied as one of the completely integrable (differential-difference) equations by algebro-geometric methods, which produced both quasi-periodic solutions in terms of theta functions of hyperelliptic curves and periodic solutions defined on suitable Jacobians by the Lax-pair method. In this work, we revisit Toda’s original approach to give solutions of the Toda lattice in terms...

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