Orbits of smooth rational curves on Enriques surfaces

2025/07/10 by Simon Brandhorst, Brandhorst, Simon, Víctor González‐Alonso +1
Computer Science · Mathematics · #14J28 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2507.07516

openalex publication_date 2025/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a closed formula for the number of orbits of smooth rational curves under the automorphism group of an Enriques surface in terms of its Nikulin root invariant and its Vinberg group.

Citations

• 527 elliptic fibrations on Enriques surfaces
• Enriques surfaces of zero entropy
• Automorphism groups of certain Enriques surfaces
• On automorphisms and the cone conjecture for Enriques surfaces in odd characteristic
• Automorphisms of supersingular K3 surfaces and Salem polynomials

Related

• Automorphism groups of certain Enriques surfaces
• Singular rational curves on Enriques surfaces
• 12 rational curves on Enriques surfaces
• A brief introduction to Enriques surfaces
• Enriques Surfaces and jacobian elliptic K3 surfaces