Weierstrass meets Enriques

作者：Braun A P^*; Ebert R; Hebecker A; Valandro R

来源：The Journal of High Energy Physics, 2010, 2010(2): 077.

DOI：10.1007/JHEP02(2010)077

• F-Theory
• Differential and Algebraic Geometry

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.

• 出版日期2010-2