Galois Groups in Enumerative Geometry and Applications

2021/08/17 by Sottile, Frank, Yahl, Thomas · 3 citations
#14M25 #65H10 #65H20 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2108.07905

Abstract

As Jordan observed in 1870, just as univariate polynomials have Galois groups, so do problems in enumerative geometry. Despite this pedigree, the study of Galois groups in enumerative geometry was dormant for a century, with a systematic study only occuring in the past 15 years. We discuss the current directions of this study, including open problems and conjectures.

Cited by

• Galois Groups of Symmetric Cubic Surfaces
• Numerically Computing Galois Groups of Minimal Problems
• Stacks, Monodromy and Symmetric Cubic Surfaces

Related

• Galois theory and Diophantine geometry
• Galois representations
• Enumerative Galois theory for number fields
• The Evolution of Enumerative Geometry: A Narrative from Classical Problems to Enriched Invariants
• Galois Theory