# Geometric aspects of Newton-Okounkov bodies

## TL;DR

This survey explores the geometric properties of Newton-Okounkov bodies in projective geometry, emphasizing how they relate to the positivity of divisors and their significance in understanding algebraic varieties.

## Contribution

It provides a comprehensive overview of the geometric aspects of Newton-Okounkov bodies and their connection to divisor positivity in algebraic geometry.

## Key findings

- Newton-Okounkov bodies encode positivity properties of divisors.
- They serve as a bridge between convex geometry and algebraic geometry.
- The survey highlights key results and open problems in the field.

## Abstract

This is a survey article on Newton-Okounkov bodies in projective geometry focusing on the relationship between positivity of divisors and Newton-Okounkov bodies.