2 research outputs found
A Strange Family of Calabi-Yau 3-folds
We study the predictions of mirror symmetry for the 1-parameter family of
Calabi-Yau 3-folds with hodge numbers
constructed in \cite{BN}. We calculate the Picard-Fuchs differential equation
associated to this family, and use it to predict the instanton numbers on the
hypothetical mirror. These exhibit a strange vanishing in odd degrees. We also
calculate the monodromy action on H^3(\tilde{X},\QQ) and find that it
strangely predicts a positive Euler characteristic for its mirror. From a
degenerate fiber of our family we construct a new rigid Calabi-Yau 3-fold. In
an appendix we prove the expansion of the conifold period conjectured in
\cite{ES} to hold for all 1-parameter families.Comment: 23 page