Measuring Singularities with Frobenius: the Basics


The multiplicity is perhaps the most naive measurement of singularities. Because f is singular at x if all the first order partial derivatives of f vanish there, it is natural to say that f is even more singular if also all the second order partials vanish, and so forth. The order, or multiplicity, of the singularity at x is the largest d such that for all differential operators ∂ of order less than d, ∂f vanishes at x. Choosing coordinates so that x is the origin, it is easy to see that the multiplicity is simply the degree of the lowest degree term of f .

1 Figure or Table

Cite this paper

@inproceedings{BENITO2012MeasuringSW, title={Measuring Singularities with Frobenius: the Basics}, author={ANG{\'E}LICA BENITO and ELEONORE FABER and KAREN E. SMITH}, year={2012} }