Non-archimedean periods for log calabi-yau surfaces
File(s)
Author(s)
Karwa, Soham
Type
Thesis
Abstract
Non-archimedean geometry has proven to be a very powerful technique to study classical problems in algebraic geometry. Whilst non-archimedean analytic spaces can be very complicated, there exists a canonical combinatorial subspace, called the essential skeleton, which retains a lot of geometric information. In this thesis, we explore how much information the skeleton of a non-archimedean analytic space captures. Our methods are directly inspired by mirror symmetry and the SYZ conjecture, in which non-archimedean geometry plays a fascinating role as first observed by Kontsevich and Soibelman.
Using the non-archimedean SYZ fibration, we study the notion of non-archimedean periods on the essential skeleton as introduced by Kontsevich and Soibelman. We prove that the non-archimedean period map recovers the analytic periods for log Calabi-Yau surfaces, verifying a conjecture of Kontsevich and Soibelman in this case.
Using the non-archimedean SYZ fibration, we study the notion of non-archimedean periods on the essential skeleton as introduced by Kontsevich and Soibelman. We prove that the non-archimedean period map recovers the analytic periods for log Calabi-Yau surfaces, verifying a conjecture of Kontsevich and Soibelman in this case.
Version
Open Access
Date Issued
2024-06-29
Date Awarded
01/02/2025
License URL
Advisor
Nicaise, Johannes
Thomas, Richard
Sponsor
Engineering and Physical Sciences Research Council
Grant Number
EP/S021590/1
Publisher Department
Department of Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)