Linear series, degenerations, and curve geometry beyond the complex numbers

• Grant number: 23/05614-9
• Support Opportunities: Regular Research Grants
• Start date: October 01, 2023
• End date: September 30, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Ethan Guy Cotterill
• Grantee: Ethan Guy Cotterill
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This research project focuses on the behavior of linear series on curves in two nontraditional contexts, in which the curves are either singular or defined over fields other than the complex numbers. Using tools from non-Archimedean geometry, A1-homotopy theory, and matroidal combinatorics, the present project aims to establish new arithmetic and singular versions of Brill--Noether theory analogous to the classical theory for smooth complex curves. (AU)