eprintid: 10204909
rev_number: 12
eprint_status: archive
userid: 699
dir: disk0/10/20/49/09
datestamp: 2025-03-13 10:22:00
lastmod: 2025-03-13 10:22:00
status_changed: 2025-03-13 10:22:00
type: thesis
metadata_visibility: show
sword_depositor: 699
creators_name: Voegtli, Pascale
title: On an extension of two classical theorems to the realm of foliations
ispublished: unpub
divisions: UCL
divisions: B04
divisions: C06
divisions: F59
note: Copyright © The Author 2025. 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 focuses on two papers that I have contributed to in the last four years. The broader scope of both projects is the birational geometry of the foliated varieties. The first part of the thesis covers joint work with D. Jiao on an extension of Kawamata's theorem on the type of morphism connecting different Minimal Models to threefolds equipped with a corank one foliation with mild singularities. The second part deals with joint work with D. Jiao and Chen on the existence of $\mathbb{Q}$-complements, a particular kind of global sections of the pluricanonical system $-mK_{\mathcal{F}}$ for some $m \in \mathbb{Z}$, for algebraically integrable log Fano foliations $\mathcal{F}$. The latter work is motivated by the groundbreaking results of Birkar on complements for Fano-type varieties which set the stage for his later success in resolving a long-standing conjecture concerning the boundedness of $\epsilon$-log canonical Fano varieties.\\
 The thesis is subdivided into two almost self-contained chapters - each dealing with one of the above-outlined theorems.
date: 2025-02-28
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: 2362478
lyricists_name: Voegtli, Pascale
lyricists_id: PVOEG64
actors_name: Voegtli, Pascale
actors_id: PVOEG64
actors_role: owner
full_text_status: public
pagerange: 1-75
pages: 76
institution: UCL(University College London)
department: Mathematics
thesis_type: Doctoral
citation:        Voegtli, Pascale;      (2025)    On an extension of two classical theorems to the realm of foliations.                   Doctoral thesis  (Ph.D), UCL(University College London).     Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/10204909/1/On_an_extension_of_two_classical_theorems_to_the_realm_of_foliations__1_%20%287%29.pdf