2022/05/23 by Hayato Morimura, Morimura, Hayato
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2205.11268
openalex publication_date 2022/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove a sort of reconstruction theorem for generic elliptic Calabi-Yau 3-folds in the sense of Căldăraru. From our argument it follows that two generic elliptic Calabi-Yau 3-folds are derived-equivalent linear over the base if and only if their generic fibers are derived-equivalent. As an application, we give affirmative answers to the conjectures raised by Knapp-Scheidegger-Schimannek. Namely, for each pair of elliptic Calabi-Yau 3-folds in their list we prove that they share the relative Jacobian and are P2-linear derived-equivalent.