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Hard Lefschetz properties and distribution of spectra in singularity theory and Ehrhart theory

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.

preprint2021arXivOpen access
Antoine Douai
math.AG
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Antoine Douai

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