Thema der Dissertation:
Toric Newton-Okounkov Functions, the Kingman Coalescent, and Fully Mixed Cells
Thema der Disputation:
Polyhedral Adjunction Theory
Toric Newton-Okounkov Functions, the Kingman Coalescent, and Fully Mixed Cells
Thema der Disputation:
Polyhedral Adjunction Theory
Abstract: Classical adjunction theory is an area of algebraic geometry, which has played a
fundamental role in the classification of projective varieties. Inspired by this, the correspondence
between polarized toric varieties and lattice polytopes provides a natural ground for an adjunction
theory of lattice polytopes. Given a rational polytope, we will introduce the main object of interest, its
adjoint polytope and study two associated geometric invariants, namely its Q-codegree and its nef
value. This leads to a decomposition theorem for polytopes with high Q-codegree, which is closely
related to the Cayley-conjecture. We will illustrate this result and give an idea of connections with
other areas.
fundamental role in the classification of projective varieties. Inspired by this, the correspondence
between polarized toric varieties and lattice polytopes provides a natural ground for an adjunction
theory of lattice polytopes. Given a rational polytope, we will introduce the main object of interest, its
adjoint polytope and study two associated geometric invariants, namely its Q-codegree and its nef
value. This leads to a decomposition theorem for polytopes with high Q-codegree, which is closely
related to the Cayley-conjecture. We will illustrate this result and give an idea of connections with
other areas.
Zeit & Ort
04.05.2021 | 09:00