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Lefschetz Properties of complete intersesctions and maximal variation of hyperplane sections

  • Mats Boij
  • Juan C. Migliore
  • Rosa M. Miró-Roig
  • Uwe Nagel
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Abstract

For an artinian complete intersection of forms of degree d, we prove that the multiplication by a general linear form is injective up to degree (3d−1)/2, independently of the number of variables. This is accomplished using algebraic and geometric properties of the union of two complete intersection curves and their general hyperplane sections. As a consequence, we solve, for any d≥ 4, the problem about the maximal variation of the hyperplane sections of a smooth hypersurface of degree d posed by A. Beauville.

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Cite

BibTeXRIS
BibTeX
@misc{boij2026lefschetz,
  title = {{Lefschetz Properties of complete intersesctions and maximal variation of hyperplane sections}},
  author = {Mats Boij and Juan C. Migliore and Rosa M. Miró-Roig and Uwe Nagel},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25521},
  eprint = {2610.25521},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25521},
}
RIS
TY  - UNPB
TI  - Lefschetz Properties of complete intersesctions and maximal variation of hyperplane sections
AU  - Mats Boij
AU  - Juan C. Migliore
AU  - Rosa M. Miró-Roig
AU  - Uwe Nagel
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.25521
UR  - https://arxiv.org/abs/2610.25521
AB  - For an artinian complete intersection of forms of degree d, we prove that the multiplication by a general linear form is injective up to degree (3d−1)/2, independently of the number of variables. This is accomplished using algebraic and geometric properties of the union of two complete intersection curves and their general hyperplane sections. As a consequence, we solve, for any d≥ 4, the problem about the maximal variation of the hyperplane sections of a smooth hypersurface of degree d posed by A. Beauville.
ER  -