Krs and Determinantal Ideals

Krs and Determinantal Ideals

Krs and Powers of Determinantal Ideals

The goal of this paper is to determine Gröbner bases of powers of determinantal ideals and to show that the Rees algebras of (products of) determinantal ideals are normal and CohenMacaulay if the characteristic of the base field is non-exceptional. Our main combinatorial result is a generalization of Schensted’s Theorem on the Knuth–Robinson–Schensted correspondence. Mathematics Subject Classif...

And Aldo Conca

We give an introduction to the theory of determinantal ideals and rings, their Gröbner bases, initial ideals and algebras, respectively. The approach is based on the straightening law and the Knuth-Robinson-Schensted correspondence. The article contains a section treating the basic results about the passage to initial ideals and algebras. Let K be a field and X an m×n matrix of indeterminates o...

GRÖBNER BASES AND DETERMINANTAL IDEALS -- An Introduction

We give an introduction to the theory of determinantal ideals and rings, their Gröbner bases, initial ideals and algebras, respectively. The approach is based on the straightening law and the Knuth-Robinson-Schensted correspondence. The article contains a section treating the basic results about the passage to initial ideals and algebras. Let K be a field and X an m × n matrix of indeterminates...

Nice Initial Complexes of Some Classical Ideals

This is a survey article on Gorenstein initial complexes of extensively studied ideals in commutative algebra and algebraic geometry. These include defining ideals of Segre and Veronese varieties, toric deformations of flag varieties known as Hibi ideals, determinantal ideals of generic matrices of indeterminates, and ideals generated by Pfaffians of generic skew symmetric matrices. We give a s...