论文标题
有效的除数和牛顿·科恩科夫的牛头杂货方案的身体
Effective divisors and Newton-Okounkov bodies of Hilbert schemes of points on toric surfaces
论文作者
论文摘要
我们在$ \ Mathbb C^2 $上计算了希尔伯特方案的（无界）牛顿 - 科恩科夫的（无界）。我们为希尔伯特（Hilbert of Hilbert）方案的牛顿 - 科恩科夫（Newton-Okounkov）机构提供了一个上界，该方案在任何光滑的圆磨表面上。我们推测，这种上限与$ \ Mathbb p^2 $，$ \ Mathbb P^1 \ times \ times \ Mathbb p^1 $和Hirzebruch表面上的Hilbert Shemes of Soints of Soints of Soints of Soints of Soints of Soints的确切界限相吻合。这些结果暗示着这些希尔伯特方案的有效锥的上限，在上述情况下，这些方案在上述情况下也是敏锐的。
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.
