Residual Intersections and Core of Modules

TL;DR

This paper introduces residual intersections for modules, proves their existence, and extends core formulas to a broader class of modules, revealing new Cohen-Macaulay properties and providing concrete examples.

Contribution

It defines residual intersections for modules, proves their existence, and extends core formulas to orientable modules with specific homological conditions.

Findings

Projective dimension one modules have Cohen-Macaulay residual intersections

A formula for the core of certain orientable modules is established

Examples of modules satisfying the assumptions are provided

Abstract

We introduce the notion of residual intersections of modules and prove their existence. We show that projective dimension one modules have Cohen-Macaulay residual intersections, namely they satisfy the relevant Artin-Nagata property. We then establish a formula for the core of orientable modules satisfying certain homological conditions, extending previous results of Corso, Polini, and Ulrich on the core of projective one modules. Finally, we provide examples of classes of modules that satisfy our assumptions.