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

2022/03/06 by Ian Cavey, Cavey, Ian · 1 citation
Mathematics · #Commutative Algebra and Its Applications #Algebraic Geometry and Number Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2203.02843

Abstract

We compute the (unbounded) Newton-Okounkov body of the Hilbert scheme of points on \mathbb C². 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 P², \mathbb P¹×\mathbb P¹, 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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