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arXiv · 0907.2691

Weierstrass meets Enriques

Andreas P. Braun·Rainer Ebert·Arthur Hebecker·Roberto Valandro
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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.

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Andreas P. Braun, Rainer Ebert, Arthur Hebecker, Roberto Valandro. 2009-07-15. Weierstrass meets Enriques. https://doi.org/10.1007/jhep02(2010)077

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