Geodesic
Vanishing cycles on Poisson varieties
Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 2, pp. 70-78 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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.
Keywords: vanishing cycles, Poisson varieties, Uhlenbeck spaces, double affine Grassmannian. 
@article{FAA_2015_49_2_a6,
     author = {D. V. Kubrak and M. V. Finkel'berg},
     title = {Vanishing cycles on {Poisson} varieties},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {70--78},
     year = {2015},
     volume = {49},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2015_49_2_a6/}
}
TY  - JOUR
AU  - D. V. Kubrak
AU  - M. V. Finkel'berg
TI  - Vanishing cycles on Poisson varieties
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2015
SP  - 70
EP  - 78
VL  - 49
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/FAA_2015_49_2_a6/
LA  - ru
ID  - FAA_2015_49_2_a6
ER  - 
%0 Journal Article
%A D. V. Kubrak
%A M. V. Finkel'berg
%T Vanishing cycles on Poisson varieties
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2015
%P 70-78
%V 49
%N 2
%U http://geodesic.mathdoc.fr/item/FAA_2015_49_2_a6/
%G ru
%F FAA_2015_49_2_a6
D. V. Kubrak; M. V. Finkel'berg. Vanishing cycles on Poisson varieties. Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 2, pp. 70-78. http://geodesic.mathdoc.fr/item/FAA_2015_49_2_a6/

[1] A. Braverman, M. Finkelberg, D. Gaitsgory, “Uhlenbeck spaces via affine Lie algebras”, The Unity of Mathematics, Progress in Math., 244, Birkhäuser, Boston, MA, 2006, 17–135 ; Erratum: arXiv: math/0301176v4 | DOI | MR | Zbl

[2] A. Braverman, M. Finkelberg, “Pursuing the double affine Grassmannian. I. Transversal slices via instantons on $A_k$-singularities”, Duke Math. J., 152:2 (2010), 175–206 | DOI | MR | Zbl

[3] S. Evens, I. Mirković, “Characteristic cycles for the loop Grassmannian and nilpotent orbits”, Duke Math. J., 97:1 (1999), 109–126 | DOI | MR | Zbl

[4] M. Kasivara, P. Shapira, Puchki na mnogoobraziyakh, Mir, M., 1997

[5] D. Maulik, A. Okounkov, Quantum Groups and Quantum Cohomology, arXiv: 1211.1287

[6] N. Proudfoot, B. Webster, “Intersection cohomology of hyperthoric varieties”, J. Algebraic Geom., 16:1 (2007), 39–63 | DOI | MR | Zbl

[7] R. Steinberg, Conjugacy Classes in Algebraic Groups, Lect. Notes Math., 366, Springer-Verlag, Berlin–New York, 1974 | DOI | MR | Zbl