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The degeneration of the Grassmannian into a toric variety and the calculation of the eigenspaces of a torus action. (English) Zbl 1346.14119
Summary: Using the method of degenerating a Grassmannian into a toric variety, we calculate formulas for the dimensions of the eigenspaces of the action of an $$n$$-dimensional torus on a Grassmannian of planes in an $$n$$-dimensional space.

##### MSC:
 14M25 Toric varieties, Newton polyhedra, Okounkov bodies 14L30 Group actions on varieties or schemes (quotients) 14M15 Grassmannians, Schubert varieties, flag manifolds 14C20 Divisors, linear systems, invertible sheaves
##### Keywords:
toric variety; Grassmannian; Poincare-Hilbert series
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