Reducible Calabi-Yau threefolds with countably many rational curves
arXiv:1802.00108
Abstract
We give a class of examples of reducible (d-semistable) threefolds of CY type with two irreducible components for which (it is reasonably easy to prove that) no family of admissible genus zero stable maps sweeps out a surface, yet such stable maps occur in infinitely many degrees.
arXiv comment8 pages. Comments welcome!