Poincaré series of curves on rational surface singularities | Zendy

Antonio Campillo | Zendy; F. Delgado | Zendy; S. M. Guseĭn-Zade | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Poincaré series of curves on rational surface singularities

Author(s) -

Antonio Campillo,

F. Delgado,

S. M. Guseĭn-Zade

Publication year - 2005

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.4171/cmh/6

Subject(s) - mathematics , singularity , poincaré series , series (stratigraphy) , gravitational singularity , surface (topology) , ring (chemistry) , essential singularity , euler characteristic , pure mathematics , rational surface , polynomial , euler's formula , mathematical analysis , function (biology) , geometry , paleontology , chemistry , physics , plasma , organic chemistry , quantum mechanics , biology , evolutionary biology

For a reducible curve singularity embedded in a rational surface singularity the Poincare series is computed. Here the Poincare series is defined by the multi-index filtration on the local ring defined by orders of a function on the branches of the curve. The method of the computations is based on the notion of the integral with respect to the Euler characteristic over the projectivization of the ring of functions (notion similar to, and inspired by, the notion of motivic integration). For the case of the E_8 surface singularity it appears that the Poincare series coincides with the Alexander polynomial of the corresponding link

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research