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Birational Geometry of Moduli Spaces via the Essential Skeleton

Offered By: IMSA via YouTube

Tags

Birational Geometry Courses Algebraic Geometry Courses Moduli Space Courses Tropical Geometry Courses

Course Description

Overview

Explore the intricate world of birational geometry and moduli spaces in this 53-minute lecture by Morgan Brown from the University of Miami. Delve into the concept of the essential skeleton, a polyhedral complex within the Berkovich analytification of a variety X over a valued field K. Discover how this powerful tool connects birational geometry with tropical geometry, focusing primarily on the moduli space $\mathcal{M}_{0,n}$. Examine topics such as dual complexes, space evaluations, tropicalization, and tropical compactification. Gain insights into log canonical models and their applications. Conclude with speculative discussions on higher-dimensional cases, particularly moduli spaces of hyperplane arrangements in $\mathbb{P}^2$, and participate in a Q&A session to further explore this fascinating mathematical domain.

Syllabus

Intro
Alphaeyes
Dual Complex
Space Evaluations
Essential Skeleton
Examples
Tropicalization
Tropical Compactification
Log Canonical Models
Questions


Taught by

IMSA

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