Igor Krichever

activity

20012017

most citedElliptic Families of Solutions of the Kadomtsev-Petviashvili Equation and the Field Elliptic Calogero-Moser System

4 citations · 13 across the 6 of their papers we have counts for

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5 papers · 1 filter

math.AG2017

Real-normalized differentials: limits on stable curves

Samuel Grushevsky, Igor Krichever, Chaya Norton

We study the behavior of real-normalized (RN) meromorphic differentials on Riemann surfaces under degeneration. We determine all possible limits of RN differentials in degenerating…

math.AG2014★ 2 cited

Commuting difference operators and the combinatorial Gale transform

I. Krichever

We study the spectral theory of $n$ -periodic strictly triangular difference operators $L = T^{- k - 1} + \sum_{j = 1}^{k} a_{i}^{j} T^{- j}$ and the spectral theory of the "superperiodic" operator…

math.AG2012★ 2 cited

Real normalized differentials and compact cycles in the moduli space of curves

I. Krichever

Using constructions of the Whitham perturbation theory of integrable system we prove a new sharp upper bound of $3 g /2 - 2$ on the dimension of complete subvarieties of $\M_g^{ct}$.

math.AG2011★ 1 cited

Real normalized differentials and Arbarello's conjecture

I. Krichever

Using meromorphic differentials with real periods, we prove Arbarello's conjecture: any compact complex cycle of dimension $g - n$ in the moduli space $\M_g$ of smooth genus $g$ alge…

math.AG2005★ 2 cited

Characterizing Jacobians via flexes of the Kummer variety

E. Arbarello, G. Marini, I. Krichever

Given an abelian variety $X$ and a point $a \in X$ we denote by $< a >$ the closure of the subgroup of $X$ generated by $a$ . Let $N = 2^{g} - 1$ . We denote by $κ: X\to κ(X)\subset\mathbb P^…