The compactified jacobian can be nonreduced

TL;DR

This paper provides an explicit example demonstrating that the compactified Jacobian of a rational space curve can be nonreduced, answering a long-standing question in algebraic geometry.

Contribution

It presents the first explicit example of a nonreduced compactified Jacobian, resolving a question posed in 1979.

Findings

The compactified Jacobian can be nonreduced for certain rational space curves.

An explicit example of a genus 4 rational space curve is constructed.

The result settles a question about the structure of compactified Jacobians.

Abstract

We prove by explicit example that the compactified jacobian can be nonreduced. The example is a rational space curve of arithmetic genus 4. This answers a question posed by Cyril D'Souza in 1979.