What type of study is this?

This is a Quantitative Study study.

October 13, 2025Open Access

Nef cones of Hilbert schemes of points on some K3 surfaces

Key Points

The nef cone of the Hilbert scheme X[n] was computed using Bridgeland stability methods, showing intricate geometric properties.
For large n, the nef cone of the nested Hilbert scheme X[n,n+1] exhibits behaviors linked to Mori dream surfaces.
Exploration of the rational map X[2] to Q[2] uncovered bounds on the nef cone for small n, highlighting structural relationships.
Study on the K3 surface with Picard rank 2 emphasizes the interplay between algebraic geometry and stability conditions.

Abstract

Let X be a Mori dream K3 surface of Picard rank 2. We compute the nef cone of the Hilbert scheme X^n of n points on X for large n using Bridgeland stability methods. We also find bounds on the nef cone for small n. Studying the geometry of a 2-to-1 cover X Q of a smooth quadric Q in P³, and its induced rational map X^2 Q^2 on the Hilbert schemes, we calculate the nef cone of X^2 in a particular case. Finally, we also find the nef cone of the nested Hilbert scheme X^n, n+1 for large n.

Read Full Paperexternally

AI से पूछें

Bookmark

View Full Paper