On Mori dreamness of blowups along space curves

Tiago Duarte Guerreiro; Sokratis Zikas

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arXiv · 2509.10148

On Mori dreamness of blowups along space curves

Tiago Duarte Guerreiro·Sokratis Zikas

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Abstract

We study the problem of determining when the blowup $X \to \mathbb{P}^3$ along a smooth space curve $C$ is a Mori Dream Space. We obtain sufficient conditions, as well obstructions to the Mori dreamness of $X$ based on the external geometry of $C$. We furthermore find infinitely many pairs $(g,d)$ such that the corresponding Hilbert schemes $H_{g,d}^S$ admit components whose general element has these obstructions. As a consequence we show that Mori dreamness is not an open property in flat families and exhibit various degenerational pathologies.

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Tiago Duarte Guerreiro, Sokratis Zikas. 2025-09-12. On Mori dreamness of blowups along space curves. https://arxiv.org/abs/2509.10148

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