Calabi–Yau Conifold Expansions

  • Slawomir CynkEmail author
  • Duco van Straten
Part of the Fields Institute Communications book series (FIC, volume 67)


We describe examples of computations of Picard–Fuchs operators for families of Calabi–Yau manifolds based on the expansion of a period near a conifold point. We find examples of operators without a point of maximal unipotent monodromy, thus answering a question posed by J. Rohde.

Key words

Calabi–Yau threefolds Picard–Fuchs operator Maximal unipotent monodromy Conifold point 

Mathematics Subject Classifications (2010)

Primary 14J32 Secondary 14Qxx 32S40 34M15 



We would like to thank the organisers for inviting us to the Workshop on Arithmetic and Geometry of K3 surfaces and Calabi–Yau threefolds held in the period 16–25 August 2011 at the Fields Institute. We also thank M. Bogner and J. Hofmann for help with the analysis of the examples. Furthermore, I thank G. Almkvist and W. Zudilin for continued interest in this crazy project. Part of this research was done during the stay of the first named author as a guest professor at the Schwerpunkt Polen of the Johannes Gutenberg–Universität in Mainz.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Institut für MathematikJohannes Gutenberg UniversityMainzGermany
  2. 2.Institut of MathematicsJagiellonian UniversityKrakówPoland

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