On a conjecture of Teissier: the case of log canonical thresholds

Abstract

For a smooth germ of algebraic variety $(X,0)$ and a hypersurface $(f=0)$ in $X$, with an isolated singularity at $0$, Teissier conjectured a lower bound for the Arnold exponent of $f$ in terms of the Arnold exponent of a hyperplane section $f\vert_H$ and the invariant $\theta_0(f)$ of the hypersurface. By building on an approach due to Loeser, we prove the conjecture in the case of log canonical thresholds.