On the Hodge structure of elliptically fibered Calabi-Yau threefolds

Abstract

The Hodge numbers of generic elliptically fibered Calabi-Yau threefolds over toric base surfaces fill out the "shield" structure previously identified by Kreuzer and Skarke. The connectivity structure of these spaces and bounds on the Hodge numbers are illuminated by considerations from F-theory and the minimal model program. In particular, there is a rigorous bound on the Hodge number h_{21} <= 491 for any elliptically fibered Calabi-Yau threefold. The threefolds with the largest known Hodge numbers are associated with a sequence of blow-ups of toric bases beginning with the Hirzebruch surface F_{12} and ending with the toric base for the F-theory model with largest known gauge group.

16 pages, 4 figures; v2: minor corrections, references added; v3: minor corrections, improvements, reference added, version for JHEP

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• Global aspects of the space of 6D N = 1 supergravities
• 6D supergravity without tensor multiplets
• TASI Lectures on Supergravity and String Vacua in Various Dimensions

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