
## 3. Calabi-Yau manifolds

1. #### Problem 3.1.

When can the elliptic genus be defined for noncompact Calabi-Yau manifolds?
• #### Problem 3.2.

Is there an index theoretic interpretation of elliptic genus? When it can, how do we compute it and what is the geometric interpretation of the coefficients? Check that this matches CFT calculations.
• #### Problem 3.3.

When can modular forms on Calabi Yau 3-folds moduli spaces be reduced to lower dimensional forms?
• #### Problem 3.4.

Investigate the role of paramodular groups in counting problems in Calabi Yau 3-folds

Cite this as: AimPL: Gromov-Witten invariants and number theory, available at http://aimpl.org/gromwitnumthry.