Asian Journal of Mathematics

Volume 26 (2022)

Number 4

On the global moduli of Calabi–Yau threefolds

Pages: 585 – 612



Ron Donagi (Department of Mathematics, David Rittenhouse Lab., University of Pennsylvania, Philadelphia, Penn., U.S.A.)

Mark Macerato (Department of Mathematics, University of California, Berkeley, Calif., U.S.A.)

Eric Sharpe (Department of Physics Virginia Tech, Blacksburg, Va., U.S.A.)


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. 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.


Calabi–Yau, moduli space, Hodge line bundle, Bagger–Witten

2010 Mathematics Subject Classification

14D23, 14J32

Received 25 February 2022

Accepted 22 June 2022

Published 24 March 2023