Zobrazeno 1 - 10
of 38
pro vyhledávání: '"Krichever, Igor"'
Autor:
Krichever, Igor, Takhtajan, Leon
For the case of algebraic curves - compact Riemann surfaces - it is shown that de Rham cohomology group $H^{1}_{\mathrm{dR}}(X,\mathbb{C})$ of a genus $g$ Riemann surface $X$ has a natural structure of a symplectic vector space. Every choice of a non
Externí odkaz:
http://arxiv.org/abs/2311.04440
Autor:
Krichever, Igor
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 certain circle of ideas and methods which show that the characterization o
Externí odkaz:
http://arxiv.org/abs/2202.04585
Autor:
Krichever, Igor
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 form of each of these characterizations is the statement that such Jacob
Externí odkaz:
http://arxiv.org/abs/2109.13161
Autor:
Krichever, Igor, Nekrasov, Nikita
Publikováno v:
SIGMA 18 (2022), 006, 37 pages
We show that Novikov-Veselov hierarchy provides a complete family of commuting symmetries of two-dimensional $O(N)$ sigma model. In the first part of the paper we use these symmetries to prove that the Fermi spectral curve for the double-periodic sig
Externí odkaz:
http://arxiv.org/abs/2106.14201
Autor:
Krichever, Igor, Nekrasov, Nikita
We study two dimensional path integral Lefschetz thimbles, i.e. the possible path integration contours. Specifically, in the examples of the $O(N)$ and ${\bf CP}^{N-1}$ models, we find a large class of complex critical points of the sigma model actio
Externí odkaz:
http://arxiv.org/abs/2010.15575
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 with prescribed orders of their poles form real orbifolds whose topology
Externí odkaz:
http://arxiv.org/abs/2010.09358
Autor:
Krichever, Igor, Varchenko, Alexander
We consider the space of solutions of the Bethe ansatz equations of the $\widehat{\frak{sl}_N}$ XXX quantum integrable model, associated with the trivial representation of $\widehat{\frak{sl}_N}$. We construct a family of commuting flows on this spac
Externí odkaz:
http://arxiv.org/abs/1907.12198
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 sequences of smooth curves, and describe the limit in terms of soluti
Externí odkaz:
http://arxiv.org/abs/1703.07806
Autor:
Krichever, Igor, Ilyina, Anna
New reductions of the 2D Toda equations associated with low-triangular difference operators are proposed. Their explicit Hamiltonian description is obtained.
Comment: Misprints are corrected,26 pages, Latex
Comment: Misprints are corrected,26 pages, Latex
Externí odkaz:
http://arxiv.org/abs/1609.05120
Autor:
Grushevsky, Samuel, Krichever, Igor
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 paper we survey the relevant constructions and show how they are rela
Externí odkaz:
http://arxiv.org/abs/1108.4211