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Regular version of the site
Of all publications in the section: 8
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Article
Khoroshkin S. M., Пакуляк С. З. Kyoto Journal of Mathematics. 2008. Vol. 48. No. 2. P. 277-321.
Added: Oct 15, 2012
Article
Kuwabara T. Kyoto Journal of Mathematics. 2008. No. 48. P. 167-217.
Added: Oct 18, 2012
Article
Michael Finkelberg, Feigin E., Reineke M. Kyoto Journal of Mathematics. 2017. Vol. 57. No. 2. P. 445-474.

  We study the connection between the affine degenerate Grassmannians in type A, quiver Grassmannians for one vertex loop quivers and affine Schubert varieties. We give an explicit description of the degenerate affine Grassmannian of type GL(n) and identify it with semi-infinite orbit closure of type A_{2n-1}. We show that principal quiver Grassmannians for the one vertex loop quiver provide finite-dimensional approximations of the degenerate affine Grassmannian. Finally, we give an explicit description of the degenerate affine Grassmannian of type A_1^{(1)}, propose a conjectural description in the symplectic case and discuss the generalization to the case of the affine degenerate flag varieties.

Added: May 10, 2017
Article
Kuznetsov A., Debarre O. Kyoto Journal of Mathematics. 2019. Vol. 4. No. 59. P. 897-953.

Beauville and Donagi proved in 1985 that the primitive middle cohomology of a smooth complex cubic 4-fold and the primitive second cohomology of its variety of lines, a smooth hyper-Kähler 4-fold, are isomorphic as polarized integral Hodge structures. We prove analogous statements for smooth complex Gushel–Mukai varieties of dimension 4 (resp., 6), that is, smooth dimensionally transverse intersections of the cone over the Grassmannian Gr(2,5), a quadric, and two hyperplanes (resp., of the cone over Gr(2,5) and a quadric). The associated hyper-Kähler 4-fold is in both cases a smooth double cover of a hypersurface in P^5 called an Eisenbud–Popescu–Walter sextic.

Added: May 10, 2020
Article
Prokhorov Y. Kyoto Journal of Mathematics. 2019. Vol. 59. No. 4. P. 1041-1073.

We classify del Pezzo surfaces of Picard number one with log canonical singularities admitting Q-Gorenstein smoothings.

Added: Aug 1, 2017
Article
Zaev D., Kolesnikov A. Kyoto Journal of Mathematics. 2017. Vol. 57. No. 2. P. 293-324.

We consider probability measures on R∞ and study optimal transportation mappings for the case of infinite Kantorovich distance. Our examples include 1) quasi-product measures, 2) measures with certain symmetric properties, in particular, exchangeable and stationary measures. We show in the latter case that existence problem for optimal transportation is closely related to ergodicity of the target measure. In particular, we prove existence of the symmetric optimal transportation for a certain class of stationary Gibbs measures.

 

Added: Dec 30, 2017
Article
Feigin B. L., Jimbo M., Miwa T. et al. Kyoto Journal of Mathematics. 2012. Vol. 52. No. 3. P. 621-659.

In this, the third paper of the series, we construct a large family of representations of the quantum toroidal gl(1)-algebra whose bases are parameterized by plane partitions with various boundary conditions and restrictions. We study the corresponding formal characters. As an application We obtain a Gelfand-Zetlin-type basis for a class of irreducible lowest weight gl(infinity)-modules.

Added: Feb 5, 2013
Article
Bogachev V., Kolesnikov A. Kyoto Journal of Mathematics. 2013. Vol. 53. No. 4. P. 713-738.

Numerous applications of the optimal transportation theory in finite-dimensional spaces have been found during the last decade. They include differential equations, probability theory, and geometry. The situation in infinite-dimensional spaces has been much less studied. However, some partial results on existence, uniqueness, and regularity have been obtained in recent papers of D. Feyel, A.S. Ustunel, M. Zakai, and the authors.

In this paper we study regularity properties of the infinite-dimensional transportation of measures on the Wiener space, where the transportation cost is given by the integral squared Cameron-Martin norm, the target measure is the Wiener measure, and the source measure is absolutely continuous with respect to the Wiener measure. Assuming that the density has the finite Fisher information (belongs to a certain Sobolev class), we prove that the potential of the corresponding optimal transportation belongs to the second (weighted) Sobolev space W^{2,2}. Some estimates involving higher-order derivatives are given. This result settles a long-standing problem and is of principal importance for the whole area of infinite-dimensional optimal transport and its applications in stochastic analysis and measure theory in infinite dimensions.

Added: Feb 26, 2014