Bialgebraic varieties of the Gamma function

2025/09/29 by Sebastian Eterović, Adele Padgett, Eterović, Sebastian +2
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Advanced Topics in Algebra #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2509.24982

Abstract

We characterize the bialgebraic varieties of the Γ function, that is, if V,W⊆ℂⁿ are irreducible affine algebraic variety which satisfy dim V =dim W and Γ(V)⊆ W, then the equations defining V (and hence also W) either give an equality between coordinates, or set some coordinates to be constant.

Citations

• The Carlitz module and a differential Ax-Lindemann-Weierstrass theorem for the Euler gamma function
• Definability of complex functions in o-minimal structures
• A differential approach to Ax-Schanuel, I
• The Ax-Schanuel conjecture for variations of mixed Hodge structures
• Ax-Lindemann-Weierstrass with derivatives and the genus 0 Fuchsian\n groups
• Ax-Schanuel for Shimura varieties
• Ax–Schanuel for the j-function

Related

• Gamma conjecture I for flag varieties
• Derived equivalence, Albanese varieties, and the zeta functions of\n 3-dimensional varieties
• Characterizing Varieties Using Birational Transformations
• On the birational geometry of varieties of maximal Albanese dimension
• Exercises in the birational geometry of algebraic varieties