Weierstrass models of elliptic toric \(K3\) hypersurfaces and symplectic cuts. (English) Zbl 1291.81313

Grassi, Antonella; Perduca, Vittorio

Adv. Theor. Math. Phys. 17, No. 4, 741-770 (2013).

Summary: We study elliptically fibered \(K3\) surfaces, with sections, in toric Fano 3-folds which satisfy certain combinatorial properties relevant to F-theory/heterotic duality. We show that some of these conditions are equivalent to the existence of an appropriate notion of a Weierstrass model adapted to the toric context. Moreover, we show that if in addition other conditions are satisfied, there exists a toric semistable degeneration of the elliptic \(K3\) surface which is compatible with the elliptic fibration and F-theory/Heterotic duality.

MSC:

81T30	String and superstring theories; other extended objects (e.g., branes) in quantum field theory
14J28	\(K3\) surfaces and Enriques surfaces
14J27	Elliptic surfaces, elliptic or Calabi-Yau fibrations

Software:

SageMath