Skip to content
DraconiticResearch
Search Sources API
181,713 studies31 sourcesUpdated 1 h ago
PreprintarXiv licencearXiv

Indeterminacy of period map and Griffiths heights for hypersurfaces

  • Sung Gi Park
Open at sourcePDFDOICite

Abstract

We prove that the period map 𝒫̅, from the GIT moduli space of degree d hypersurface X in ℙn to the Baily-Borel compactification of the period image associated to the middle cohomology Hn−1prim(X,ℤ), extends regularly to X if and only if X has at worst nodal singularities (resp. suspensions of slc surface singularities) when n is even (resp. n is odd). This verifies and generalizes Laza-O'Grady's prediction on the indeterminacy locus of the period map for quartic K3s to arbitrary hypersurfaces. For Calabi-Yau hypersurfaces, we prove that the birational map from the GIT moduli space to the BBH compactification extends regularly to X if and only if X has semi-log canonical singularities. The results apply to distinguish the Baily-Borel and BBH compactifications. In the process, we answer two questions of Mordant on the Griffiths height for families of hypersurfaces over curves, which are crucial to the proofs of the main results.

Related

  1. Stacky Heights, Entropy, and Zeta Functions of Weighted Hypersurfaces over Finite Fields
    S. Salami, T. Shaska
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  2. On Quantum Indeterminacy and the Uncertainty Principle
    Maurice de Gosson
    arXivPreprintarXiv licenceFull textGeometry & topologyMathematical physicsarXiv
  3. Ample vector bundles without Griffiths-semipositive metrics
    Yun-Heng Du, Song-Yan Xie
    arXivPreprintarXiv licenceFull textAlgebra & number theoryAnalysis & PDEsarXiv
  4. Griffiths positivity does not imply positivity of the top Chern form
    Yun-Heng Du
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. A first-jet characterization of Griffiths positivity
    Yun-Heng Du, Song-Yan Xie
    arXivPreprintarXiv licenceFull textAlgebra & number theoryAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{park2026indeterminacy,
  title = {{Indeterminacy of period map and Griffiths heights for hypersurfaces}},
  author = {Sung Gi Park},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.34429},
  eprint = {2610.34429},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.34429},
}
RIS
TY  - UNPB
TI  - Indeterminacy of period map and Griffiths heights for hypersurfaces
AU  - Sung Gi Park
PY  - 2026
DA  - 2026/10/25
PB  - arXiv
DO  - 10.48550/arxiv.2610.34429
UR  - https://arxiv.org/abs/2610.34429
AB  - We prove that the period map 𝒫̅, from the GIT moduli space of degree d hypersurface X in ℙ^n to the Baily-Borel compactification of the period image associated to the middle cohomology H^n−1_prim(X,ℤ), extends regularly to X if and only if X has at worst nodal singularities (resp. suspensions of slc surface singularities) when n is even (resp. n is odd). This verifies and generalizes Laza-O'Grady's prediction on the indeterminacy locus of the period map for quartic K3s to arbitrary hypersurfaces. For Calabi-Yau hypersurfaces, we prove that the birational map from the GIT moduli space to the BBH compactification extends regularly to X if and only if X has semi-log canonical singularities. The results apply to distinguish the Baily-Borel and BBH compactifications. In the process, we answer two questions of Mordant on the Griffiths height for families of hypersurfaces over curves, which are crucial to the proofs of the main results.
ER  -