The set of jumping conics of a locally free sheaf of dimension 2 on $P^2$

TL;DR

This paper investigates the set of jumping conics for a rank 2 sheaf on the projective plane, showing it forms a maximal determinantal variety of a skew form and exploring its properties.

Contribution

It introduces the concept of jumping conics for sheaves on P^2 and characterizes their set as a maximal determinantal variety, providing new insights into their structure.

Findings

The set of jumping conics is a maximal determinantal variety.

Properties of the associated skew form are established.

The structure of jumping conics is linked to determinantal varieties.

Abstract

We consider a locally free sheaf $F$ of dimension 2 on $P^2$. A conic $q$ on $P^2$ is called a jumping conic if the restriction of $F$ to $q$ is not the generic one. We prove that the set of jumping conics is the maximal determinantal variety of a skew form. Some properties of this skew form are found.