The Poincare series of multiplier ideals of a simple complete ideal in a local ring of a smooth surface

Details The Poincare series of multiplier ideals of a simple complete ideal in a local ring of a smooth surface The Poincare series of multiplier ideals of a simple complete ideal in a local ring of a smooth surface

2008-06-02

arxiv.org/abs/0806.0231v3

Mathematics

Algebraic Geometry

Scientific paper

For a simple complete ideal $\wp$ of a local ring at a closed point on a smooth complex algebraic surface, we introduce an algebraic object, named Poincar\'e series $P_{\wp}$, that gathers in an unified way the jumping numbers and the dimensions of the vector space quotients given by consecutive multiplier ideals attached to $\wp$. This paper is devoted to prove that $P_{\wp}$ is a rational function giving an explicit expression for it.

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