Poincare series of a toric variety

Details Poincare series of a toric variety Poincare series of a toric variety

2006-10-16

arxiv.org/abs/math/0610473v1

Mathematics

Algebraic Geometry

Scientific paper

For an affine toric variety X we compute the Poincare series of the multi-index filtration defined by a finite number of monomial divisorial valuations on the ring O_{X,0}. We give an alternative description of the Poincare series as an integral with respect to the Euler characteristic over the projectivization of the space of germs O_{X,0}. In particular we study divisorial valuations on the ring O_{C^d,0} that arise by considering toric constellations. We give an explicit formula for the Poincare series and a nice geometric description. This generalizes an expression of the Poincare series for curves and rational surface singularities.

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