English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We prove that the topological type of a normal surface singularity $(X,0)$provides finite bounds for the multiplicity and polar multiplicity of $(X,0)$,as well as for the combinatorics of the families of generic hyperplane sectionsand of polar curves of the generic plane projections of $(X,0)$. A keyingredient in our proof is a topological bound of the growth of the Matherdiscrepancies of $(X,0)$, which allows us to bound the number of point blowupsnecessary to achieve factorization of any resolution of $(X,0)$ through itsNash transform. This fits in the program of polar explorations, the quest todetermine the generic polar variety of a singular surface germ, to which thefinal part of the paper is devoted.

Polar exploration of complex surface germs