Statut | Confirmé |
Série | MATH-IHES |
Domaines | math |
Date | Vendredi 22 Mars 2019 |
Heure | 11:00 |
Institut | IHES |
Salle | Amphithéâtre Léon Motchane |
Nom de l'orateur | Adiprasito |
Prenom de l'orateur | Karim |
Addresse email de l'orateur | |
Institution de l'orateur | Hebrew University of Jerusalem & IHES |
Titre | Combinatorial Lefschetz Theorems Beyond Positivity |
Résumé | Consider a simplicial complex that allows for an embedding into R^d. How many faces of dimension d/2or higher can it have? How dense can they be? This basic question goes back to Descartes' "Lost Theorem" and Euler's work on polyhedra. Using it and other fundamental combinatorial problems, we introduce a version of the Kähler package beyond positivity, allowing us to prove the hard Lefschetz theorem for toric varieties (and beyond) even when the ample cone is empty. A particular focus lies on replacing the Hodge-Riemann relations by a non-degeneracy relation at torus-invariant subspaces, allowing us to state and prove a generalization of theorems of Hall and Laman in the setting of toric varieties and, more generally, the face rings of Hochster, Reisner and Stanley. This has several applications including full characterization of the possible face numbers of simplicial rational homology spheres, a generalization of the crossing lemma.) |
Numéro de preprint arXiv | |
Commentaires | |
Fichiers attachés |
Pour obtenir l' affiche de ce séminaire : [ Postscript | PDF ]
|
[ English version ] |