Jet bundles on Gorenstein curves and applications

TL;DR

This survey reviews constructions of locally free replacements for the sheaf of principal parts on Gorenstein curves, discusses related literature, and explores applications to classical enumerative geometry problems.

Contribution

It provides a comprehensive catalogue of these constructions and connects them to classical problems in Enumerative Algebraic Geometry.

Findings

Catalogues various constructions of locally free replacements.

Discusses the literature and historical development.

Highlights applications to classical enumerative problems.

Abstract

In the last twenty years a number of papers appeared aiming to construct locally free replacements of the sheaf of principal parts for families of Gorenstein curves. The main goal of this survey is to present to the widest possible audience of mathematical readers a catalogue of such constructions, discussing the related literature and reporting on a few applications to classical problems in Enumerative Algebraic Geometry.