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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 $P_{d,m}(T)=\binom{T+m}{m}-\binom{T+m-d}{m}$.

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