A Transcendence Criterion for CM on Some Families of Calabi–Yau Manifolds Academic Article uri icon


  • In this chapter, we give some examples of the validity of a special case of a recent conjecture of Green et al. (Ann. Math. Studies, no. 183, Princeton University Press, 2012). This special case is an analogue of a celebrated theorem of Schneider (Math. Annalen 113:1-13, 1937) on the transcendence of values of the elliptic modular function and its generalization in Cohen (RockyMountain J. Math. 26:987-1001, 1996) and Shiga and Wolfart (J. Reine Angew. Math. 463:1-25, 1995). Related techniques apply to all the examples of CMCY families in the work of Rohde (Lecture Notes in Mathematics 1975, Springer, Berlin, 2009), and this is the subject of a paper in preparation by the author (Tretkoff, Transcendence and CM on Borcea-Voisin towers of Calabi-Yau manifolds). © Springer Science+Business Media New York 2013.

author list (cited authors)

  • Tretkoff, P., & Tretkoff, M. D.

citation count

  • 2

publication date

  • July 2012