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PreprintCC BY 4.0arXiv

Algebraic ellipticity of double covers of (P1)3

  • Alexander Dvorsky
  • Shulim Kaliman
  • Mikhail Zaidenberg
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Abstract

We show that every smooth complex double cover of (P1)3 branched along a smooth divisor of tridegree (2,2,2) is algebraically Gromov elliptic. These irrational Fano threefolds form Mori--Mukai family 3-1 and have anticanonical genus seven and Picard rank three. Their three coordinate projections define degree-four del Pezzo fibrations. Each threefold also admits a dominant rational map of degree two from P3.

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Cite

BibTeXRIS
BibTeX
@misc{dvorsky2026algebraic,
  title = {{Algebraic ellipticity of double covers of $(\mathbf P^1)^3$}},
  author = {Alexander Dvorsky and Shulim Kaliman and Mikhail Zaidenberg},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04983},
  eprint = {2611.04983},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04983},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Algebraic ellipticity of double covers of (P^1)^3
AU  - Alexander Dvorsky
AU  - Shulim Kaliman
AU  - Mikhail Zaidenberg
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04983
UR  - https://arxiv.org/abs/2611.04983
AB  - We show that every smooth complex double cover of (P^1)^3 branched along a smooth divisor of tridegree (2,2,2) is algebraically Gromov elliptic. These irrational Fano threefolds form Mori--Mukai family 3-1 and have anticanonical genus seven and Picard rank three. Their three coordinate projections define degree-four del Pezzo fibrations. Each threefold also admits a dominant rational map of degree two from P^3.
ER  -