Hard Lefschetz properties and distribution of spectra in singularity theory and Ehrhart theory
Résumé
We discuss the distribution of the spectrum at infinity of a convenient and nondegenerate Laurent polynomial (singularity side) and the distribution of the Newton spectrum of a polytope (Ehrhart theory side). To this end, we study a hard Lefschetz property for Laurent polynomials and for polytopes and we give combinatorial criteria for this property to be true. This provides informations about a conjecture by Katzarkov-Kontsevitch-Pantev.