Determinantal Ideals of Square Linear Matrices

Part I: General oversight.- Background steps in determinantal rings.- Algebraic preliminaries.- Geometric oversight.- Part II: Linear section of notable structured square matrices.- Linear sections of the generic square matrix.- Symmetry preserving linear sections of the generic symmetric matrix.- Linear sections of the generic square Hankel matrix.- Hankel like catalecticants.- The dual variety of a linear determinantal hypersurface.- Part III: Other classes of linear sections.- Hilbert-Burch linear sections.- Apocryphal classes.- Appendix.- Index.

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• Álgebra
• Geometria algébrica

determinantal ideals;square linear matrices;submaximal minors;Hessian determinant;polar map;gradient ideal;homaloidal polynomial;1-generic matrix;dual variety;ladder ideal;Cohen-Macaulay