Alexander polynomials and Poincar, series of sets of ideals

作者：Gusein Zade S M^*; Delgado F; Campillo A

来源：Functional Analysis and Its Applications, 2011, 45(4): 271-277.

DOI：10.1007/s10688-011-0029-2

• ideal
• surface
• Poincare series
• zeta function

Earlier the authors considered and, in some cases, computed Poincar, series for two sorts of multi-index filtrations on the ring of germs of functions on a complex (normal) surface singularity (in particular, on the complex plane). A filtration of the first class was defined by a curve (with several branches) on the surface singularity. A filtration of the second class (called divisorial) was defined by a set of components of the exceptional divisor of a modification of the surface singularity. Here we define and compute in some cases the Poincar, series corresponding to a set of ideals in the ring of germs of functions on a surface singularity. For the complex plane, this notion unites the two classes of filtrations described above.

• 出版日期2011-12