Smoothing Calabi-Yau threefolds with nodes and del Pezzo cone points

@misc{wuebben2026smoothing,
  title = {{Smoothing Calabi-Yau threefolds with nodes and del Pezzo cone points}},
  author = {Bernd Johannes Wuebben},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35915},
  eprint = {2610.35915},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35915},
}

TY  - UNPB
TI  - Smoothing Calabi-Yau threefolds with nodes and del Pezzo cone points
AU  - Bernd Johannes Wuebben
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.35915
UR  - https://arxiv.org/abs/2610.35915
AB  - We give a necessary and sufficient homological criterion for smoothing projective Calabi-Yau threefolds with nodes and anticanonical cones over smooth del Pezzo surfaces of degrees five, six and seven, or over a smooth quadric surface. For some choice of local smoothing components, the criterion requires a relation on a crepant resolution among link classes whose associated local parameters avoid every discriminant. The complexified relation space describes first-order deformations modulo locally trivial ones. Necessity follows from local period and vanishing-cycle arguments; sufficiency applies Friedman's unobstructedness theorem to a crepant partial resolution. Whenever the criterion holds, the deformation space on the chosen components is smooth. A nonsmoothable example, whose deformation space is reduced with four smooth components, shows why nonvanishing at every singular point is insufficient. We also construct a smoothable Batyrev hypersurface admitting no smoothing induced by proper ambient families obtained from Minkowski decompositions at a single lattice degree.
ER  -