Frobenius determinants and Toric varieties

Abstract: Given a finite group $G$ of order $n>1$ and variables $(X_g)_{g\in G}$ the Frobenius or group-determinant is by definition $\Theta(G)((X_g)_{g\in G}):=\det((X_{gh^{-1}})_{(g,h)\in G\times G})$. We associate to every Frobenius determinant of a finite abelian group of order $n\geqslant3$ a toric variety. We also study along the way its singular points and determine the number of its hyper-surfaces.

analysis of PDEsclassical analysis and ODEscomplex variablesdifferential geometrydynamical systemsfunctional analysismetric geometry

Audience: researchers in the topic

Analysis and Geometry Seminar