477 citations · 904 across the 38 of their papers we have counts for
10 papers · 1 filter
Abelian pole systems and Riemann-Schottky type systems
Igor Krichever
In this survey of works on a characterization of Jacobians and Prym varieties among indecomposable principally polarized abelian varieties via the soliton theory we focus on a cert…
Characterizing Jacobians of algebraic curves with involution
Igor Krichever
We give two characterizations of Jacobians of curves with involution having fixed points in the framework of two particular cases of Welter's trisecant conjecture. The geometric fo…
Real-normalized differentials with a single order pole
Igor Krichever, Sergei Lando, Alexandra Skripchenko
A meromorphic differential on a Riemann surface is said to be {\it real-normalized} if all its periods are real. Real-normalized differentials on Riemann surfaces of given genus wi…
Amoebas, Ronkin function and Monge-Ampère measures of algebraic curves with marked points
I. Krichever
A generalization of the amoeba and the Ronkin function of a plane algebraic curve for a pair of harmonic functions on an algebraic curve with punctures is proposed. Extremal proper…
Soliton equations and the Riemann-Schottky problem
I. Krichever, T. Shiota
Novikov's conjecture on the Riemann-Schottky problem: {\it the Jacobians of smooth algebraic curves are precisely those indecomposable principally polarized abelian varieties (ppav…
Real-normalized differentials and the elliptic Calogero-Moser system
Samuel Grushevsky, Igor Krichever
In our recent works we have used meromorphic differentials on Riemann surfaces all of whose periods are real to study the geometry of the moduli spaces of Riemann surfaces. In this…