Nef cone decompositions for nested Hilbert schemes of points on surfaces

Chiwon Yoon

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arXiv · 2608.26922

Nef cone decompositions for nested Hilbert schemes of points on surfaces

Chiwon Yoon

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Abstract

Let $S$ be a smooth projective surface with $q(S)=0$. We give numerical criteria for the nef cones of $S^{[n,n+1]}$ and $S^{[1,n]}$ to decompose as sums of pullbacks of nef cones under their natural morphisms. These criteria recover the known decompositions for the projective plane, Hirzebruch surfaces, and Picard rank one K3 surfaces, and apply to del Pezzo surfaces with $2\le K_S^2\le7$. For a del Pezzo surface of degree one, we show that the corresponding pullback decompositions fail for both $S^{[n,n+1]}$ and $S^{[1,n]}$.

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Chiwon Yoon. 2026-08-27. Nef cone decompositions for nested Hilbert schemes of points on surfaces. https://arxiv.org/abs/2608.26922

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