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PreprintCC BY 4.0arXiv

Nodal deformations of hypersurfaces with an ordinary m-fold point

  • Remke Kloosterman
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Abstract

Let X⊂ 𝕆n be a nodal hypersurface of degree d with an ordinary m-fold point. Let δX be the largest value of δ such that X is contained in the closure of the Severi variety of degree d hypersurface in ℙn with δ nodes. After recalling how the semicontinuity of the spectrum yields an upper bound for δX, we produce various lower bounds for δX. These bounds are given by polynomials in m of degree n, with different leading coefficients. This improves previous bounds given by Ciliberto-Galati.

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Cite

BibTeXRIS
BibTeX
@misc{kloosterman2026nodal,
  title = {{Nodal deformations of hypersurfaces with an ordinary $m$-fold point}},
  author = {Remke Kloosterman},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18313},
  eprint = {2609.18313},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.18313},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Nodal deformations of hypersurfaces with an ordinary m-fold point
AU  - Remke Kloosterman
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.18313
UR  - https://arxiv.org/abs/2609.18313
AB  - Let X⊂ 𝕆^n be a nodal hypersurface of degree d with an ordinary m-fold point. Let δ_X be the largest value of δ such that X is contained in the closure of the Severi variety of degree d hypersurface in ℙ^n with δ nodes. After recalling how the semicontinuity of the spectrum yields an upper bound for δ_X, we produce various lower bounds for δ_X. These bounds are given by polynomials in m of degree n, with different leading coefficients. This improves previous bounds given by Ciliberto-Galati.
ER  -