Finiteness of rational curves of degree 12 on a general quintic threefold

TL;DR

This paper proves that a generic quintic threefold contains only finitely many smooth rational curves of degree 12, confirming a prediction related to Clemens' conjecture.

Contribution

It establishes the finiteness of degree 12 rational curves on a general quintic threefold, advancing understanding of rational curves on Calabi-Yau threefolds.

Findings

Finiteness of smooth rational curves of degree 12 on a general quintic threefold.

Supports Clemens' conjecture predictions.

Advances knowledge of rational curves in algebraic geometry.

Abstract

We prove the following statement, predicted by Clemens' conjecture: A generic quintic threefold contains only finitely many smooth rational curves of degree 12.