Weierstrass meets Enriques

TL;DR

This paper investigates the degeneration of K3 surfaces to T^4/Z_2, providing explicit lattice embeddings and analyzing the Enriques involution's action on elliptic K3 surfaces, with implications for F-theory models.

Contribution

It introduces two methods for embedding the lattice of collapsed cycles of T^4/Z_2 into K3, enhancing understanding of K3 degenerations and Enriques involutions.

Findings

Explicit lattice embeddings of T^4/Z_2 into K3

Description of degeneration via Wilson lines

Enriques involution acts consistently in F-theory limit

Abstract

We study in detail the degeneration of K3 to T^4/Z_2. We obtain an explicit embedding of the lattice of collapsed cycles of T^4/Z_2 into the lattice of integral cycles of K3 in two different ways. Our first method exploits the duality to the heterotic string on T^3. This allows us to describe the degeneration in terms of Wilson lines. Our second method is based on the blow-up of T^4/Z_2. From this blow-up, we directly construct the full lattice of integral cycles of K3. Finally, we use our results to describe the action of the Enriques involution on elliptic K3 surfaces, finding that a Weierstrass model description is consistent with the Enriques involution only in the F-theory limit.