Stability of fibrations over one-dimensional bases

Abban, Hamid; Fedorchuk, Maksym; Krylov, Igor

Abstract

We introduce and study a new notion of stability for varieties fibered over curves, motivated by Kollár’s stability for homogeneous polynomials with integral coefficients. We develop tools to study geometric properties of stable birational models of fibrations whose fibers are complete intersections in weighted projective spaces. As an application, we prove the existence of standard models of threefold degree 1 del Pezzo fibrations, settling a conjecture of Corti.

Citation

Abban, H., Fedorchuk, M., & Krylov, I. (2022). Stability of fibrations over one-dimensional bases. Duke Mathematical Journal, 171(12), 2461-2518. https://doi.org/10.1215/00127094-2022-0025

• Journal Article Type: Article
• Acceptance Date: Jun 9, 2022
• Online Publication Date: Jun 9, 2022
• Publication Date: Sep 1, 2022
• Deposit Date: Mar 17, 2025
• Journal: Duke Mathematical Journal
• Print ISSN: 0012-7094
• Electronic ISSN: 1547-7398
• Publisher: Duke University Press
• Peer Reviewed: Peer Reviewed
• Volume: 171
• Issue: 12
• Pages: 2461-2518
• DOI: https://doi.org/10.1215/00127094-2022-0025
• Keywords: birational geometry of threefolds , del Pezzo fibrations , Kollár stability , stability of fibrations
• Public URL: https://nottingham-repository.worktribe.com/output/46731479
• Publisher URL: https://projecteuclid.org/journals/duke-mathematical-journal/volume-171/issue-12/Stability-of-fibrations-over-one-dimensional-bases/10.1215/00127094-2022-0025.full