2023/04/03 by Giuseppe Ancona, Mattia Cavicchi, Ancona, Giuseppe +5 · 1 citation
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #14C25 #14J42 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2304.00978
openalex publication_date 2023/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the hyper-Kähler varieties of OG10-type constructed by Laza-Saccà-Voisin (LSV) verify the Lefschetz standard conjecture. This is an application of a more general result, stating that certain Lagrangian fibrations verify this conjecture. The main technical assumption of this general result is that the Lagrangian fibration satisfies the hypotheses of Ngô's support theorem. Verifying that the LSV tenfolds do satisfy those hypotheses is of independent interest. Another point of independent interest of the paper is the definition and the study of the Lefschetz standard conjecture in the relative setting, and its relation to the classical absolute case.