Poincare series of a toric variety
Algebraic Geometry
2007-05-23 v1 Commutative Algebra
Abstract
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.
Keywords
Cite
@article{arxiv.math/0610473,
title = {Poincare series of a toric variety},
author = {Ann Lemahieu},
journal= {arXiv preprint arXiv:math/0610473},
year = {2007}
}