Classification of sextic curves in the Fano 3-fold V₅ with rational Galois covers in \mathbb P³

2025/04/19 by Chi, Quo-Shin, Xie, Zhenxiao, Xu, Yan
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2504.14168

Abstract

In this paper, we classify sextic curves in the Fano 3-fold \bf V₅ (the smooth quintic del Pezzo 3-fold) that admit rational Galois covers in the complex \mathbb P³. 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 V₅ through their Galois covers in \mathbb P³.

Citations

• Fano 3-folds and classification of constantly curved holomorphic 2-spheres of degree 6 in the complex Grassmannian G(2,5)
• Constant curvature solutions of Grassmannian sigma models: (1) Holomorphic solutions
• Constant curvature solutions of Grassmannian sigma models: (2) Non-holomorphic solutions
• Spin curves and Scorza quartics
• Algebraic Curves and Riemann Surfaces
• Isometric Imbedding of Complex Manifolds
• Harmonic maps into Lie groups: classical solutions of the chiral model
• Minimal immersions of surfaces in Euclidean spheres

Related

• Fano 3-folds and classification of constantly curved holomorphic 2-spheres of degree 6 in the complex Grassmannian G(2,5)
• Rational Curves on Coindex 3 Fano Varieties
• Moduli spaces of rational curves on Fano threefolds
• Rational curves on prime Fano threefolds of index 1
• Geometric Manin's Conjecture for Fano 3-Folds