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Nef cone decompositions for nested Hilbert schemes of points on surfaces
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≤ KS2≤7. 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].
Related
- Hochschild cohomology of Hilbert schemes of points on surfaces
- Non-reducedness of the Hilbert schemes of few points
- The canonical class and Chern character operators on Hilbert schemes of points
- Stability conditions on products of curves and Hilbert schemes of surfaces
- Log-concavity and unimodality of Hodge numbers of Hilbert schemes of points over a surface
BibTeX
@misc{yoon2026cone,
title = {{Nef cone decompositions for nested Hilbert schemes of points on surfaces}},
author = {Chiwon Yoon},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.26922},
eprint = {2608.26922},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.26922},
}
RIS
TY - UNPB
TI - Nef cone decompositions for nested Hilbert schemes of points on surfaces
AU - Chiwon Yoon
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2608.26922
UR - https://arxiv.org/abs/2608.26922
AB - 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≤ K_S^2≤7. 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].
ER -