Weierstrass meets Enriques
arXiv:0907.2691 · doi:10.1007/JHEP02(2010)077
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.
35 pages, 9 figures
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- Tate Form and Weak Coupling Limits in F-theory
- Towards Generalized Mirror Symmetry for Twisted Connected Sum Manifolds
- F-theory duals of singular heterotic K3 mode
- Restrictions on infinite sequences of type IIB vacua
- Voisin-Borcea Manifolds and Heterotic Orbifold Models