Calabi-Yau threefolds with large h[superscript 2,1]
Author(s)Johnson, Samuel Buck; Taylor, Washington
Calabi-Yau threefolds with large h 2,1
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We carry out a systematic analysis of Calabi-Yau threefolds that are elliptically fibered with section (“EFS”) and have a large Hodge number h[superscript 2,1]. EFS Calabi-Yau threefolds live in a single connected space, with regions of moduli space associated with different topologies connected through transitions that can be understood in terms of singular Weierstrass models. We determine the complete set of such threefolds that have h[superscript 2,1] ≥ 350 by tuning coefficients in Weierstrass models over Hirzebruch surfaces. The resulting set of Hodge numbers includes those of all known Calabi-Yau threefolds with h[superscript 2,1] ≥ 350, as well as three apparently new Calabi-Yau threefolds. We speculate that there are no other Calabi-Yau threefolds (elliptically fibered or not) with Hodge numbers that exceed this bound. We summarize the theoretical and practical obstacles to a complete enumeration of all possible EFS Calabi-Yau threefolds and fourfolds, including those with small Hodge numbers, using this approach.
DepartmentMassachusetts Institute of Technology. Center for Theoretical Physics; Massachusetts Institute of Technology. Department of Physics
Journal of High Energy Physics
Springer-Verlag/International School for Advanced Studies (SISSA)
Johnson, Samuel B., and Washington Taylor. “Calabi-Yau Threefolds with Large h [superscript 2,1].” J. High Energ. Phys. 2014, no. 10 (October 2014).
Final published version