Weierstrass meets Enriques
High Energy Physics - Theory
2010-03-02 v1
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.
Cite
@article{arxiv.0907.2691,
title = {Weierstrass meets Enriques},
author = {Andreas P. Braun and Rainer Ebert and Arthur Hebecker and Roberto Valandro},
journal= {arXiv preprint arXiv:0907.2691},
year = {2010}
}
Comments
35 pages, 9 figures