Resolvent degree, Hilbert's 13th problem and geometry

DOI10.4171/LEM/65-3/4-2zbMath1460.14104arXiv1803.04063MaRDI QIDQ2024037

Benson Farb, Jesse Wolfson

Publication date: 3 May 2021

Published in: L'Enseignement Mathématique. 2e Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.04063

zbMATH Keywords

enumerative problemsalgebraic functionHilbert's 13th problemresolvent degree

Mathematics Subject Classification ID

Separable extensions, Galois theory (12F10) Group actions on varieties or schemes (quotients) (14L30) Enumerative problems (combinatorial problems) in algebraic geometry (14N10) Polynomials in general fields (irreducibility, etc.) (12E05) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) Coverings of curves, fundamental group (14H30) Other nonalgebraically closed ground fields in algebraic geometry (14G27)

Related Items

Modular functions and resolvent problems (with an appendix by Nate Harman), Upper bounds on resolvent degree via Sylvester's obliteration algorithm, Generalized versality, special points, and resolvent degree for the sporadic groups, The geometric average size of Selmer groups over function fields, Optimization of the richardson integration over fluctuations of its step sizes, Tschirnhaus transformations after Hilbert, From Hilbert's 13th problem to essential dimension and back

Uses Software

• ATLAS Group Representations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some consequences of the Karpenko-Merkurjev theorem.
• Configurations of lines and models of Lie algebras
• E. W. von Tschirnhaus: His role in early calculus and his work and impact on algebra
• Solving the quintic by iteration
• Galois groups of enumerative problems
• On the resolvent problem
• Any smooth plane quartic can be reconstructed from its bitangents
• Essential dimension: a survey
• Quartic curves and their bitangents
• Resolving \(G\)-torsors by abelian base extensions.
• The geometry of some special arithmetic quotients
• The algebraic equations of degrees 5, 9, 157,\dots , and the arithmetic upon an algebraic variety
• 3264 and All That
• Classical Algebraic Geometry
• Pseudo-reflection groups and essential dimension
• Moduli spaces and the inverse Galois problem for cubic surfaces
• The Galois group of the tangency problem for plane curves.
• Versality of algebraic group actions and rational points on twisted varieties
• A note on systems of homogeneous algebraic equations