Positive del Pezzo Geometry

TL;DR

This paper explores the positive geometry of del Pezzo surfaces and their moduli spaces, connecting algebraic geometry with mathematical physics through canonical forms and scattering amplitudes.

Contribution

It develops the positive geometry framework for del Pezzo surfaces, revealing their polyhedral structures, symmetries, and applications to scattering amplitudes.

Findings

Derived the connected components from polyhedral spaces with Weyl group symmetries.

Studied canonical forms and their relation to scattering amplitudes.

Solved the likelihood equations for these geometric structures.

Abstract

Real, complex, and tropical algebraic geometry join forces in a new branch of mathematical physics called positive geometry. We develop the positive geometry of del Pezzo surfaces and their moduli spaces, viewed as very affine varieties. Their connected components are derived from polyhedral spaces with Weyl group symmetries. We study their canonical forms and scattering amplitudes, and we solve the likelihood equations.