Symmetry preserving degenerations of the generic symmetric matrix

2018/02/20 by Cunha, Rainelly, Ramos, Zaqueu, Simis, Aron
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1802.08067

Abstract

One considers certain degenerations of the generic symmetric matrix over a field k of characteristic zero and the main structures related to the determinant f of the matrix, such as the ideal generated by its partial derivatives, the polar map defined by these derivatives and its image V(f), the Hessian matrix, the ideal and the map given by the cofactors, and the dual variety of V(f).

Related

• Degenerations of the generic square matrix. Polar map and determinantal structure
• Coordinate sections of generic Hankel matrices
• Minors of symmetric and exterior powers
• Gram Matrices for Isotropic Vectors
• Desingularization of generic symmetric and generic skew-symmetric determinantal singularities