On Tangent Cones of Schubert Varieties

  title={On Tangent Cones of Schubert Varieties},
  author={Dmitry Fuchs and Alexandre Kirillov and Sophie Morier-Genoud and Valentin Ovsienko},
  journal={Arnold Mathematical Journal},
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… 
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