eprintid: 10196777 rev_number: 14 eprint_status: archive userid: 699 dir: disk0/10/19/67/77 datestamp: 2024-10-10 08:07:48 lastmod: 2024-10-10 08:07:48 status_changed: 2024-10-10 08:07:48 type: thesis metadata_visibility: show sword_depositor: 699 creators_name: Benozzo, Marta title: Birational geometry of fibrations in positive characteristic: On the canonical bundle formula and the Iitaka conjectures ispublished: unpub divisions: UCL divisions: B04 divisions: C06 divisions: F59 note: Copyright © The Author 2024. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. abstract: This thesis concerns the study of fibrations between algebraic varieties over fields of positive characteristic. These are fundamental objects used to study the classification of algebraic varieties. In particular, my thesis focuses on two problems: the canonical bundle formula and the Iitaka conjectures. Let f : X \to Z be a fibration between normal projective varieties over a perfect field of positive characteristic. Assume the Minimal Model Program and the existence of log resolutions. Then, we prove that, if K_X is f-nef, Z is a curve and the general fibre has nice singularities, the moduli part is nef, up to a birational map. As a corollary, we prove nefness of the moduli part in the K-trivial case. In particular, if X has dimension 3 and is defined over a perfect field of characteristic p > 5, the canonical bundle formula holds unconditionally. We also study an Iitaka-type inequality k(X,-K_X) \leq k(X_z,-K_{X_z})+k(Z,-K_Z) for the anticanonical divisors, where X_z is a general fibre of f. We conclude that it holds when X_z has good F-singularities. Furthermore, we give counterexamples in characteristics 2 and 3 for fibrations with non-normal fibres, constructed from Tango–Raynaud surfaces. date: 2024-09-28 date_type: published oa_status: green full_text_type: other thesis_class: doctoral_open thesis_award: Ph.D language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 2311003 lyricists_name: Benozzo, Marta lyricists_id: MBENO09 actors_name: Benozzo, Marta actors_id: MBENO09 actors_role: owner full_text_status: public pages: 159 institution: UCL (University College London) department: Mathematics thesis_type: Doctoral citation: Benozzo, Marta; (2024) Birational geometry of fibrations in positive characteristic: On the canonical bundle formula and the Iitaka conjectures. Doctoral thesis (Ph.D), UCL (University College London). Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10196777/8/Benozzo_10196777_thesis_sigs_removed.pdf