Voegtli, Pascale; (2025) On an extension of two classical theorems to the realm of foliations. Doctoral thesis (Ph.D), UCL(University College London).

Preview

Text On_an_extension_of_two_classical_theorems_to_the_realm_of_foliations__1_ (7).pdf - Accepted Version Download (574kB) | Preview

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.

Download activity - last month

Export as XMLCSVJSON

Download activity - last 12 months

Export as JSONXMLCSV

Downloads by country - last 12 months

Export as JSONCSVXML

Archive Staff Only

View Item