Classification of sextic curves in the Fano 3-fold $\mathcal{V}_5$ with rational Galois covers in ${\mathbb P}^3$

Quo-Shin Chi; Zhenxiao Xie; Yan Xu

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arXiv · 2504.14168

Classification of sextic curves in the Fano 3-fold $\mathcal{V}_5$ with rational Galois covers in ${\mathbb P}^3$

Quo-Shin Chi·Zhenxiao Xie·Yan Xu

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Abstract

In this paper, we classify sextic curves in the Fano $3$-fold $\bf \mathcal{V}_5$ (the smooth quintic del Pezzo $3$-fold) that admit rational Galois covers in the complex ${\mathbb P}^3$. We show that the moduli space of such sextic curves is of complex dimension $2$ through the invariants of the engaged Galois groups for the explicit constructions. This raises the intriguing question of understanding the moduli space of sextic curves in ${\mathcal V}_5$ through their Galois covers in ${\mathbb P}^3$.

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Quo-Shin Chi, Zhenxiao Xie, Yan Xu. 2025-04-19. Classification of sextic curves in the Fano 3-fold $\mathcal{V}_5$ with rational Galois covers in ${\mathbb P}^3$. https://arxiv.org/abs/2504.14168

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