Newton Okounkov bodies for curve classes.

Doctoral student: 
LEVEY Lucie
Date de soutenance: 
Sunday, October 1, 2023
Supervisors: 
Name: 
McCLEAN Catriona
Laboratory: 
Institut Fourier
Name: 
KURONYA Alex
Laboratory: 
Universitat Frankfurt
Summary: 

The Newton Okounkov body is a recently constructed invariant associated to a divisor on a variety, which can be thought of as a partial generalisation to arbitrary varieties of the toric polytope of divisors on toric varieties. It encodes information on the asymptotic behaviour of the section ring in an easily accessible format and has been successfully used over the last decade to prove many results in various areas of algebraic geometry. Currently, no higher codimension analogue of this theory exists. The aim of this thesis will be to lay the groundwork for such a theory by studying the case of curves. After construction of an analogue of the Newton Okounkov body for curve classes, we will extend to this new context the fundamental results of the theory for divisors.