Zobrazeno 1 - 10
of 223
pro vyhledávání: '"Korotkin, D."'
Autor:
Bertola, M., Korotkin, D.
We revisit symplectic properties of the monodromy map for Fuchsian systems on the Riemann sphere. We extend previous results of Hitchin, Alekseev-Malkin and Korotkin-Samtleben where it was shown that the monodromy map is a Poisson morphism between th
Externí odkaz:
http://arxiv.org/abs/1903.09197
Autor:
Bertola, M., Korotkin, D.
The principal goal of the paper is to apply the approach inspired by the theory of integrable systems to construct explicit sections of line bundles over the combinatorial model of the moduli space of pointed Riemann surfaces based on Jenkins-Strebel
Externí odkaz:
http://arxiv.org/abs/1804.02495
Autor:
Korotkin, D., Zograf, P.
We use the formalism of the Bergman tau functions to study the geometry of moduli spaces of holomorphic quadratic differentials on complex algebraic curves. We introduce two natural tau functions and interpret them as holomorphic sections of certain
Externí odkaz:
http://arxiv.org/abs/1302.0577
Publikováno v:
Advances in Mathematics, Volume 227, Issue 1, 1 May 2011, Pages 586-600
The isomonodromic tau function of the Fuchsian differential equations associated to Frobenius structures on Hurwitz spaces can be viewed as a section of a line bundle on the space of admissible covers. We study the asymptotic behavior of the tau func
Externí odkaz:
http://arxiv.org/abs/0912.3909
Autor:
Korotkin, D., Shramchenko, V.
Publikováno v:
J. Reine Angew.Math., issue 661, 125-187 (2011)
In this paper we study the Fuchsian Riemann-Hilbert (inverse monodromy) problem corresponding to Frobenius structures on Hurwitz spaces. We find a solution to this Riemann-Hilbert problem in terms of integrals of certain meromorphic differentials ove
Externí odkaz:
http://arxiv.org/abs/0909.0543
Autor:
Korotkin, D., Samtleben, H.
Publikováno v:
Adv.Math.Phys.2009:461860,2009
The $2\times 2$ Schlesinger system for the case of four regular singularities is equivalent to the Painlev\'e VI equation. The Painlev\'e VI equation can in turn be rewritten in the symmetric form of Okamoto's equation; the dependent variable in Okam
Externí odkaz:
http://arxiv.org/abs/0906.1962
We study extremal properties of the determinant of the Laplacian in the Bergman metric on the moduli space of compact genus two Riemann surfaces. By a combination of analytical and numerical methods we identify four non-degenerate critical points of
Externí odkaz:
http://arxiv.org/abs/math/0511217
Autor:
Kokotov, A., Korotkin, D.
Let $w$ be an Abelian differential on compact Riemann surface of genus $g\geq 1$. We obtain an explicit holomorphic factorization formula for $\zeta$-regularized determinant of the Laplacian in flat conical metrics with trivial holonomy $|w|^2$, gene
Externí odkaz:
http://arxiv.org/abs/math/0405042
Autor:
Kokotov, A., Korotkin, D.
In this note we give a simple proof of the fact that the determinant of Laplace operator in smooth metric over compact Riemann surfaces of arbitrary genus $g$ monotonously grows under the normalized Ricci flow. Together with results of Hamilton that
Externí odkaz:
http://arxiv.org/abs/math/0405010