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August 2013 Weierstrass models of elliptic toric $K3$ hypersurfaces and symplectic cuts
Antonella Grassi, Vittorio Perduca
Adv. Theor. Math. Phys. 17(4): 741-770 (August 2013).


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.


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Antonella Grassi. Vittorio Perduca. "Weierstrass models of elliptic toric $K3$ hypersurfaces and symplectic cuts." Adv. Theor. Math. Phys. 17 (4) 741 - 770, August 2013.


Published: August 2013
First available in Project Euclid: 21 August 2014

zbMATH: 1291.81313
MathSciNet: MR3262515

Rights: Copyright © 2013 International Press of Boston

Vol.17 • No. 4 • August 2013
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