Celebratio Mathematica — Fuchs — Complete Bibliography

Complete Bibliography

Works connected to Valentin Yurevich Ovsienko

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D. Fuchs, A. Kirillov, S. Morier-Genoud, and V. Ovsienko: “On tangent cones of Schubert varieties,” Arnold Math. J. 3 : 4 (2017), pp. 451–482. MR 3766071 Zbl 1427.14103 ArXiv 1606.07846 article

We consider tangent cones of Schubert varieties in the complete flag variety, and investigate the problem when the tangent cones of two different Schubert varieties coincide. We give a sufficient condition for such coincidence, and formulate a conjecture that provides a necessary condition. In particular, we show that all Schubert varieties corresponding to the Coxeter elements of the Weyl group have the same tangent cone. Our main tool is the notion of pillar entries in the rank matrix counting the dimensions of the intersections of a given flag with the standard one. This notion is a version of Fulton’s essential set. We calculate the dimension of a Schubert variety in terms of the pillar entries of the rank matrix.

Sophie Morier-Genoud	Related
Alexandre Aleksandrovich Kirillov	Related
Valentin Yurevich Ovsienko	Related