# Numerical Macaulification in Arbitrary Codimension

An ideal J is said to be *numerically c-ACM *(NACM) if R/J has the Hilbert function of some codimension c ACM subscheme of P^n. We exhibit algorithm which takes an arbitrary ideal and produces, via a finite sequence of basic double links, an ideal which is numerically c-ACM. An immediate consequence of this result is that every even liaison class of equidimensional codimension c subschemes of P^n contains elements which are NACM. This was first proved for the codimension two case by Migliore and Nagel, but was an open question in higher codimension.

Let *L* denote the even liaison class of three skew lines in P^4, and let* L_S* be denote the even liaison class of three skew lines on a smooth hypersurface S in P^4 of degree at least two. We also give a complete description of the sequences of basic double links which (in S) produce curves which are NACM. We conclude by showing that the subset of *L_S* consisting of NACM subschemes, which we denote by *M_S,* fails to have the Lazarsfeld-Rao property.

## History

## Date Created

2018-07-04## Date Modified

2018-11-09## Defense Date

2018-05-11## CIP Code

- PHD-MATH

## Research Director(s)

Juan C. Migliore## Degree

- Doctor of Philosophy

## Degree Level

- Doctoral Dissertation

## Alternate Identifier

1051772011## Library Record

004943587## OCLC Number

1051772011## Program Name

- Mathematics (MATH)