On the global moduli of Calabi-Yau threefolds

Abstract

In this note we initiate a program to obtain global descriptions of Calabi-Yau moduli spaces, to calculate their Picard group, and to identify within that group the Hodge line bundle, and the closely-related Bagger-Witten line bundle. We do this here for several Calabi-Yau's obtained in [DW09] as crepant resolutions of the orbifold quotient of the product of three elliptic curves. In particular we verify in these cases a recent claim of [GHKSST16] by noting that a power of the Hodge line bundle is trivial -- even though in most of these cases the Picard group is infinite.

arXiv comment28 pages, LaTeX, 3 figures; v2: thorough revision, error corrected, added author

References in corpus (9)

• Anomalies, Conformal Manifolds, and Spheres
• On orbifolds and free fermion constructions
• Cubics, Integrable Systems, and Calabi-Yau Threefolds
• On the Number of Chiral Generations in Z2 X Z2 Orbifolds
• Lectures on Moduli Spaces of Elliptic Curves
• Intermediate Jacobians and ADE Hitchin Systems
• Type II String Theory on Calabi-Yau Manifolds with Torsion and Non-Abelian Discrete Gauge Symmetries
• The Picard groups of the stacks $Y_0(2)$ and $Y_0(3)$
• Complex K-theory of mirror pairs

Cited by in corpus (4)

• Flat Monodromies and a Moduli Space Size Conjecture
• Anomalies of Duality Groups and Extended Conformal Manifolds
• Finiteness and the Emergence of Dualities
• Global aspects of moduli spaces of 2d SCFTs