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Vanishing cycles on Poisson varieties
Functional Analysis and Its Applications. 2015. Vol. 49. No. 2. P. 135–141.
Finkelberg M. V., Kubrak D.
We slightly extend results of Evens and Mirković and “compute” the characteristic cycles of intersection cohomology sheaves on transversal slices in a double affine Grassmannian. We propose a conjecture relating the hyperbolic stalks and microlocalization at a torus-fixed point in a Poisson variety. © 2015, Springer Science+Business Media New York.
Serge Lvovski, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze 2024 Vol. XXIV No. 2 P. 941–963
Using an adjunction-theoretic result due to A. J. Sommese together with a proposition from SGA7, we obtain a complete list of smooth threefolds for which the monodromy group, acting on the second cohomology group of its smooth hyperplane section, is Z/2Z. The possibility of such a classification was announced by F. L. Zak in 1991. ...
Added: July 11, 2024
Michael Finkelberg, Schechtman V., , in: Representation Theory and Algebraic Geometry.: Switzerland: Birkhauser/Springer, 2022. P. 57–83.
Added: June 20, 2022
Victor A. Vassiliev, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 2020 Vol. 16 P. 1–21
Local diffusion of strictly hyperbolic higher-order PDE's with constant coefficients at all simple singularities of corresponding wavefronts can be explained and recognized by only two local geometrical features of these wavefronts. We radically disprove the obvious conjecture extending this fact to arbitrary singularities: namely, we present examples of diffusion at all non-simple singularity classes of generic wavefronts ...
Added: March 21, 2020
Michael Finkelberg, , in: Proceedings of the International Congress of Mathematicians 2018.: World Scientific Publishing Co. Pte. Ltd, 2019. P. 1279–1298.
We propose a conjectural construction of various slices for double affine Grassmannians as Coulomb branches of 3-dimensional N = 4 supersymmetric affine quiver
gauge theories. It generalizes the known construction for the usual affine Grassmannians, and makes sense for arbitrary symmetric Kac-Mody algebras. ...
Added: September 19, 2019
Efimov A., International Mathematics Research Notices 2018 No. 12 P. 3834–3869
In this article, we will show that for a smooth quasi-projective variety X over complex numbers, and regular function W on X, the periodic cyclic homology of the DG category of matrix factorizations of W on X is identified (under the Riemann–Hilbert correspondence) with the vanishing cohomology, with the monodromy twisted by a sign. Also, ...
Added: October 14, 2018
Kubrak D., Finkelberg M. V., Функциональный анализ и его приложения 2015 Т. 49 № 2 С. 70–78
Мы немного обобщаем результаты Мирковича-Эванса и вычисляем характеристические циклы пучков Горески-Макферсона на трансверсальных срезах в двойном аффинном грассманниане. Мы также выдвигаем гипотезу, связывающую гиперболические слои и микролокализацию в неподвижной относительно действия тора точке пуассонова многообразия. ...
Added: June 12, 2015
Serge Lvovski, Manuscripta Mathematica 2014 Vol. 145 P. 235–242
We show that using an idea from a paper by Van de Ven one may obtain a
simple proof of Zak's classification of smooth projective surfaces
with zero vanishing cycles. This method of proof allows one to extend
Zak's theorem to the case of finite characteristic. ...
Added: October 14, 2014
Lvovsky S., / Series math "arxiv.org". 2013. No. 1305.2205.
We show that using an idea from a paper by Van de Ven one may obtain a simple proof of Zak's classification of smooth projective surfaces with zero vanishing cycles. This method of proof allows one to extend Zak's theorem to the case of finite characteristic. ...
Added: October 3, 2013
Braverman A., Finkelberg M. V., Kazhdan D., Springer Proceedings in Mathematics & Statistics 2012 Vol. 9 P. 17–29
Added: February 5, 2013
Finkelberg M. V., Braverman A., Advances in Mathematics 2012 No. 230 P. 414–432
This is the second paper of the series, started by Braverman-Finkelberg (2010) which describes a conjectural analogue of the affine Grassmannian for affine Kac-Moody groups (also known as double affine Grassmannian). The current paper is dedicated to describing a conjectural analogue of the convolution diagram for the double affine Grassmannian. In case our group is ...
Added: December 3, 2012