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Bounded cohomology property on Jacobian elliptic surfaces with simplicial Mori cones

  • Sichen Li
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Abstract

Let X be a Jacobian elliptic surface with finite Mordell-Weil group and exactly one reducible fiber. We prove that if χ(𝒪X)≥ ρ(X), then the Mori cone of X is simplicial. As an application, assuming additionally q(X)=0, we show that X satisfies the bounded cohomology property (BCP): there exists a constant cX>0 such that h1(𝒪X(C))≤ cX h0(𝒪X(C)) for every curve C on X. We also establish a necessary and sufficient condition for the BCP to hold on minimal smooth projective surfaces Y with κ(Y)≥ 1, q(Y)=0, and rational polyhedral Mori cones.

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Cite

BibTeXRIS
BibTeX
@misc{li2026bounded,
  title = {{Bounded cohomology property on Jacobian elliptic surfaces with simplicial Mori cones}},
  author = {Sichen Li},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.00592},
  eprint = {2609.00592},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.00592},
}
RIS
TY  - UNPB
TI  - Bounded cohomology property on Jacobian elliptic surfaces with simplicial Mori cones
AU  - Sichen Li
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.00592
UR  - https://arxiv.org/abs/2609.00592
AB  - Let X be a Jacobian elliptic surface with finite Mordell-Weil group and exactly one reducible fiber. We prove that if χ(𝒪_X)≥ ρ(X), then the Mori cone of X is simplicial. As an application, assuming additionally q(X)=0, we show that X satisfies the bounded cohomology property (BCP): there exists a constant c_X>0 such that h^1(𝒪_X(C))≤ c_X h^0(𝒪_X(C)) for every curve C on X. We also establish a necessary and sufficient condition for the BCP to hold on minimal smooth projective surfaces Y with κ(Y)≥ 1, q(Y)=0, and rational polyhedral Mori cones.
ER  -