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PreprintCC BY 4.0arXiv

An atomic approach to Shokurov's conic-bundle conjecture

  • Leonardo F. Cavenaghi
  • Ludmil Katzarkov
  • Daniel Pomerleano
  • Zhijia Zhang
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Abstract

In this paper, we apply a weaker version of Hodge atoms to show that a standard conic bundle over a smooth complex projective rational surface S is irrational if |2KS+Δ|≠∅, where Δ is the discriminant divisor. This proves Shokurov's conjecture on rationality of conic bundle threefolds. As an application, we deduce precisely which nodal quartic double solids are rational.

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Cite

BibTeXRIS
BibTeX
@misc{cavenaghi2026atomic,
  title = {{An atomic approach to Shokurov's conic-bundle conjecture}},
  author = {Leonardo F. Cavenaghi and Ludmil Katzarkov and Daniel Pomerleano and Zhijia Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41174},
  eprint = {2610.41174},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41174},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - An atomic approach to Shokurov's conic-bundle conjecture
AU  - Leonardo F. Cavenaghi
AU  - Ludmil Katzarkov
AU  - Daniel Pomerleano
AU  - Zhijia Zhang
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41174
UR  - https://arxiv.org/abs/2610.41174
AB  - In this paper, we apply a weaker version of Hodge atoms to show that a standard conic bundle over a smooth complex projective rational surface S is irrational if |2K_S+Δ|≠∅, where Δ is the discriminant divisor. This proves Shokurov's conjecture on rationality of conic bundle threefolds. As an application, we deduce precisely which nodal quartic double solids are rational.
ER  -