The Nef cone of the Hilbert scheme of hypersurfaces in the Grassmannian

TL;DR

This paper determines the structure of the nef cone of the Hilbert scheme of hypersurfaces in Grassmannians for certain degrees and dimensions, revealing it is spanned by six specific classes.

Contribution

It explicitly describes the nef cone of the Hilbert scheme of hypersurfaces in Grassmannians for degrees d ≥ 3 and m > 2, identifying its six generating classes.

Findings

Nef cone is spanned by 6 classes in the general case

Applicable for hypersurfaces with degree d ≥ 3 and m > 2

Provides explicit geometric description of the nef cone

Abstract

We show that when $d \geq 3$ and $m>2$, the Nef cone of the Hilbert scheme $Hilb_{P_{d,m}(T)}(G(k,n))$ is a cone spanned by 6 classes in general case, where $P_{d,m}(T)=\binom{T+m}{m}-\binom{T+m-d}{m}$.