Invariants of ideals generated by pfaffians

TL;DR

This paper computes key algebraic invariants such as multiplicity and Castelnuovo-Mumford regularity for pfaffian ideals of ladders, providing explicit formulas and a recursive procedure using liaison theory.

Contribution

It introduces a recursive method and explicit formulas for invariants of pfaffian ladder ideals, advancing understanding in algebraic geometry and combinatorics.

Findings

Explicit formulas for some pfaffian ladder ideals

A recursive procedure for computing invariants

Application of liaison theory in this context

Abstract

Ideals generated by pfaffians are of interest in commutative algebra and algebraic geometry, as well as in combinatorics. In this article we compute multiplicity and Castelnuovo-Mumford regularity of pfaffian ideals of ladders. We give explicit formulas for some families of ideals, and indicate a procedure that allows to recursively compute the invariants of any pfaffian ideal of ladder. Our approach makes an essential use of liaison theory.