6 papers
Curves of infinite genus I Riemann--Roch theorem for small degree
Ilya Zakharevich
The most useful and interesting line bundles over algebraic curves of a very high genus have the ratio δof the degree to the genus close to half-integer values, usually δ\approx 0,…
Nonlinear wave equation, nonlinear Riemann problem, and the twistor transform of Veronese webs
Ilya Zakharevich
Veronese webs are rich geometric structures with deep relationships to various domains of mathematics. The PDEs which determine the Veronese web are overdetermined if dim >3, but i…
Kronecker webs, bihamiltonian structures, and the method of argument translation
Ilya Zakharevich
We show that manifolds which parameterize values of first integrals of integrable finite-dimensional bihamiltonian systems carry a geometric structure which we call a {\em Kronecke…
Webs, Lenard schemes, and the local geometry of bihamiltonian Toda and Lax structures
Israel M. Gelfand, Ilya Zakharevich
We introduce a criterion that a given bihamiltonian structure allows a local coordinate system where both brackets have constant coefficients. This criterion is applied to the biha…
Geometic vertex operators
Ilya Zakharevich
Vertex operators, being families of birational transformations of infinite-dimensional algebraic ``varieties'' M, act on appropriate line bundles on M. However, they act on (meromo…
Quasi-algebraic geometry of curves I. Riemann-Roch theorem and Jacobian
Ilya Zakharevich
We discuss an analogue of Riemann-Roch theorem for curves with an infinite number of handles. We represent such a curve X by its Shottki model, which is an open subset U of CP^{1}…