On a question of Teissier

TL;DR

This paper uses advanced algebraic geometry tools to establish an upper bound for polar invariants related to hypersurface singularities, addressing a question posed by Teissier and providing a weaker alternative to his conjectured bound.

Contribution

It introduces an upper bound for polar invariants using Demailly and Pham's results, offering a new perspective on Teissier's question.

Findings

Established an upper bound for polar invariants.

Provided a weaker alternative to Teissier's conjectured bound.

Applied log canonical thresholds to hypersurface singularities.

Abstract

Using a result of Demailly and Pham on log canonical thresholds, we give an upper bound for polar invariants from a question of Teissier on hypersurface singularities. This provides a weaker alternative upper bound compared to the one conjectured by Teissier.