Hilbert schemes of two points on K3 surfaces and certain rational cubic fourfolds

TL;DR

This paper demonstrates that for specific rational cubic fourfolds, the Fano schemes of lines are birationally equivalent to Hilbert schemes of two points on K3 surfaces, revealing a deep geometric connection.

Contribution

It establishes a birational relationship between Fano schemes of lines on certain rational cubic fourfolds and Hilbert schemes of two points on K3 surfaces, advancing understanding of their geometry.

Findings

Fano schemes of lines are birational to Hilbert schemes of two points on K3 surfaces.

Identifies specific rational cubic fourfolds with this property.

Provides new insights into the geometry of these fourfolds.

Abstract

In this paper, we check that Fano schemes of lines on certain rational cubic fourfolds are birational to Hilbert schemes of two points on K3 surfaces.