Geodesic
A GRAPHICAL CALCULUS FOR 2-BLOCK SPALTENSTEIN VARIETIES
Glasgow mathematical journal, Tome 54 (2012) no. 2, pp. 449-477

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DOI

We generalise statements known about Springer fibres associated to nilpotents with two Jordan blocks to Spaltenstein varieties. We study the geometry of generalised irreducible components (i.e. Bialynicki-Birula cells) and their pairwise intersections. In particular, we develop a graphical calculus that encodes their structure as iterated fibre bundles with CP1 as base spaces, and compute their cohomology. At the end, we present a connection with coloured cobordisms generalising the construction of Khovanov (M. Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101(3) (2000), 359–426) and Stroppel (C. Stroppel, Parabolic category O, perverse sheaves on Grassmannians, Springer fibres and Khovanov homology, Compositio Mathematica145(4) (2009), 954–992).
DOI : 10.1017/S0017089512000110
Mots-clés : Primary: 14M15, Secondary: 17B10, 18D10, 16S38 
SCHÄFER, GISA. A GRAPHICAL CALCULUS FOR 2-BLOCK SPALTENSTEIN VARIETIES. Glasgow mathematical journal, Tome 54 (2012) no. 2, pp. 449-477. doi: 10.1017/S0017089512000110
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