On birational relations among singular Fano varieties
Lead Research Organisation:
Loughborough University
Department Name: Mathematical Sciences
Abstract
Fano varieties are central in geometry. They generalise sphere in higher dimensions and appear in several applications.
A breakthrough in modern algebraic geometry is the development of the Minimal Model Program (MMP). Smoothness is a commonly assumed condition on varieties, but MMP dictates that one should consider mildly singular spaces.
In this project, we will study birational relations among Fano 3-folds that admit certain types of singularities. This sits among a bigger project that aims to explicitly classify algebraic varieties in dimension 3.
We will engage various methods, including Sarkiov program, techniques of MMP as well as method of maximal singularity, to tackle this problem.
A breakthrough in modern algebraic geometry is the development of the Minimal Model Program (MMP). Smoothness is a commonly assumed condition on varieties, but MMP dictates that one should consider mildly singular spaces.
In this project, we will study birational relations among Fano 3-folds that admit certain types of singularities. This sits among a bigger project that aims to explicitly classify algebraic varieties in dimension 3.
We will engage various methods, including Sarkiov program, techniques of MMP as well as method of maximal singularity, to tackle this problem.
Organisations
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509516/1 | 01/10/2016 | 30/09/2021 | |||
| 1820497 | Studentship | EP/N509516/1 | 01/10/2016 | 30/04/2020 | Erik Paemurru |
| Description | My research addresses a gap in the classification theory of 3-dimensional singular Fano varieties. One aim of a classification is to produce a list of representatives with nice properties. Another aim is describing the relations between these representatives. I work in the latter. My first key result is giving methods to study the relations for a certain type of singularities. The second main result is carrying out this study, that is, finding relations, for a specific class of 3-dimensional Fano varieties. |
| Exploitation Route | My research is a step towards the bigger goal of classifying 3-dimensional singular Fano varieties, with mild singularities. My result could be taken further by developing similar methods for other classes of singularities. This can be applied to study the birational geometry of any Fano 3-folds given by equations. |
| Sectors | Other |