K3 surfaces with a symplectic automorphism of order 4

2022/08/03 by Piroddi, Benedetta
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2208.01962

Abstract

Given X a K3 surface admitting a symplectic automorphism τ of order 4, we describe the isometry τ^* on H²(X,\mathbb Z). Having called Z and Y respectively the minimal resolutions of the quotient surfaces Z=X/τ² and Y=X/τ, we also describe the maps induced in cohomology by the rational quotient maps X→ Z, X→ Y and Y→ Z: with this knowledge, we are able to give a lattice-theoretic characterization of Z, and find the relation between the Néron-Severi lattices of X, Z and Y in the projective case. We also produce three different projective models for X, Z and Y, each associated to a different polarization of degree 4 on X.

Related

• K3 surfaces with non-symplectic automorphisms of 2-power order
• Symmetries of order four on K3 surfaces
• Kummer surfaces and K3 surfaces with (Z/2Z)⁴ symplectic action
• K3 surfaces with ℤ₂² symplectic action
• K3 surfaces with non-symplectic automorphisms of prime order