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arXiv · 2203.02843

Effective divisors and Newton-Okounkov bodies of Hilbert schemes of points on toric surfaces

Ian Cavey
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Abstract

We compute the (unbounded) Newton-Okounkov body of the Hilbert scheme of points on $\mathbb C^2$. We obtain an upper bound for the Newton-Okounkov body of the Hilbert scheme of points on any smooth toric surface. We conjecture that this upper bound coincides with the exact Newton-Okounkov body for the Hilbert schemes of points on $\mathbb P^2$, $\mathbb P^1\times\mathbb P^1$, and Hirzebruch surfaces. These results imply upper bounds for the effective cones of these Hilbert schemes, which are also conjecturally sharp in the above cases.

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Ian Cavey. 2022-03-06. Effective divisors and Newton-Okounkov bodies of Hilbert schemes of points on toric surfaces. https://arxiv.org/abs/2203.02843

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