Classical Algebraic Geometry and Discrete Integrable Systems
Abstract
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry side, which is applied to differential and discrete Painlev\'e equations on the integrable systems side. Along the way we also discuss the theory of resolution of indeterminacies, which is applied to the cohomological computation of algebraic entropy of birational transformations of projective spaces, which is closely related to the integrability of the discrete systems they define.
Cite
@article{arxiv.2510.12647,
title = {Classical Algebraic Geometry and Discrete Integrable Systems},
author = {Gessica Alecci and Michele Graffeo and Alexander Stokes},
journal= {arXiv preprint arXiv:2510.12647},
year = {2025}
}
Comments
80 pages, 20 figures. Lecture notes to appear on "Symmetry and Integrability of Difference Equations - Lecture notes of ASIDE15"