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