Degeneration of Calabi-Yau threefolds with Galois action induced by modular form of weight 3

@misc{oczko2026degeneration,
  title = {{Degeneration of Calabi-Yau threefolds with Galois action induced by modular form of weight 3}},
  author = {Marcin Oczko},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.35157},
  eprint = {2609.35157},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.35157},
}

TY  - UNPB
TI  - Degeneration of Calabi-Yau threefolds with Galois action induced by modular form of weight 3
AU  - Marcin Oczko
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.35157
UR  - https://arxiv.org/abs/2609.35157
AB  - We study a one-parameter family of double octic Calabi-Yau threefolds with two degenerations of type K. For each of these degenerations we construct a semistable model and compute the limiting mixed Hodge structure. We show that the ℓ-adic Galois representation on the limiting cohomology is isomorphic (up to semisimplification) to the direct sum of the Galois representation attached to a weight-three modular form associated with a singular K3 surface and its Tate twist. This gives an explicit realization of the expected relation between type K degenerations of Calabi-Yau threefolds and K3 surfaces.
ER  -