Finkelberg, M. V.; Kubrak, D. V. Vanishing cycles on Poisson varieties. (English. Russian original) Zbl 1348.14044 Funct. Anal. Appl. 49, No. 2, 135-141 (2015); translation from Funkts. Anal. Prilozh. 49, No. 2, 70-78 (2015). This paper computes the characteristic cycles of intersection cohomology sheaves on transversal slices in a double affine Grassmannian. Reviewer: Peter Crooks (Toronto) Cited in 1 ReviewCited in 1 Document MSC: 14F05 Sheaves, derived categories of sheaves, etc. (MSC2010) 14M15 Grassmannians, Schubert varieties, flag manifolds 22E67 Loop groups and related constructions, group-theoretic treatment 32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects) 53D17 Poisson manifolds; Poisson groupoids and algebroids 14F17 Vanishing theorems in algebraic geometry Keywords:vanishing cycles; Poisson varieties; Uhlenbeck spaces; double affine Grassmannian PDFBibTeX XMLCite \textit{M. V. Finkelberg} and \textit{D. V. Kubrak}, Funct. Anal. Appl. 49, No. 2, 135--141 (2015; Zbl 1348.14044); translation from Funkts. Anal. Prilozh. 49, No. 2, 70--78 (2015) Full Text: DOI arXiv References: [1] Braverman, A.; Finkelberg, M.; Gaitsgory, D., Uhlenbeck spaces via affine Lie algebras, 17-135 (2006), MA · Zbl 1105.14013 [2] A. Braverman and M. Finkelberg, “Pursuing the double affine Grassmannian. I. Transversal slices via instantons on Ak -singularities,” Duke Math. J., 152:2 (2010), 175-206. · Zbl 1200.14083 [3] S. Evens and I. Mirkovi´c, “Characteristic cycles for the loop Grassmannian and nilpotent orbits,” Duke Math. J., 97:1 (1999), 109-126. · Zbl 1160.22306 [4] M. Kashiwara and P. Schapira, Sheaves on Manifolds, 2nd ed., Grundlehren der Mathematischen Wissenschaften, vol. 292, Springer-Verlag, Berlin, 1994. · Zbl 0709.18001 [5] D. Maulik and A. Okounkov, Quantum Groups and Quantum Cohomology, http://arxiv.org/abs/1211.1287. · Zbl 1226.14069 [6] N. Proudfoot and B. Webster, “Intersection cohomology of hypertoric varieties,” J. Algebraic Geom., 16:1 (2007), 39-63. · Zbl 1119.14016 [7] Steinberg, R., Conjugacy Classes in Algebraic Groups (1974), Berlin-New York · Zbl 0281.20037 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.