The auto-Igusa zeta function of a plane curve singularity is rational
Andrew R. Stout
TL;DR
This paper proves that the auto-Igusa zeta function for plane curve singularities is rational, providing a new criterion to determine smoothness of the curve at a point over algebraically closed fields of characteristic zero.
Contribution
It establishes the rationality of the auto-Igusa zeta function for plane curve singularities, linking it to smoothness criteria.
Findings
Auto-Igusa zeta function is rational for plane curve singularities.
Rationality criterion for smoothness of plane curves.
New algebraic condition for smoothness detection.
Abstract
It is shown that the auto Igusa zeta function of the germ of a plane curve singularity is rational. This gives a new criterion for a plane curve over an algebraically closed field of characteristic zero to be smooth at a point.
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