Affine Homogeneous Surfaces with Hessian rank 2 and Algebras of Differential Invariants

2020/10/06 by Chen, Zhangchi, Merker, Joël
#53A55 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2010.02873

Abstract

Consider a graphed holomorphic surface u=F(x,y) in ℂ³_x,y,u under the action of the affine transformation group A(3). In 1999, Eastwood and Ezhov obtained a list of homogeneous models by determining possible tangential vector fields. Inspired by Olver's recurrence formulas, we study the algebra of A(3) differential invariants of surfaces. We obtain necessary conditions for homogeneity of algebraic nature. Solving these conditions, we organise homogeneous models in inequivalent branches.

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