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arXiv · 2312.07542

Line configurations and K3 surfaces

Elias Sink
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Abstract

We study the realization spaces of $10_3$ line configurations. Answering a question posed by Sturmfels in 1991, we use elliptic surface techniques to show that realizations over $\mathbb{Q}$ are dense in those over $\mathbb{R}$ for all $10_3$ configurations. We find that for exactly four of the ten configurations, the realization space admits a compactification by a K3 surface. We show that these have Picard number 20 and compute their discriminants. Finally, we use geometric invariant theory to give an elegant interpretation of these K3 surfaces as moduli spaces.

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Elias Sink. 2023-09-27. Line configurations and K3 surfaces. https://arxiv.org/abs/2312.07542

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