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Secant varieties of Segre-Veronese varieties ℙm × ℙn embedded by 𝒪(1, 2) are non-defective for n ≫ m3, m ≥ 3

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2026

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Ken, Nikhil

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http://nbn-resolving.de/urn:nbn:de:bsz:352-2-lrc0cd8hj6hg9
DOI (zitierfähiger Link)
https://doi.org/10.1016/j.jsc.2025.102546
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CC BY 4.0

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European Union (EU): 101120296 (TENORS)

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Open Access Hybrid

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Mathematik und Statistik: Publikationen
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Journal of Symbolic Computation. Elsevier. 2026, 135, 102546. ISSN 0747-7171. eISSN 1095-855X. Verfügbar unter: doi: 10.1016/j.jsc.2025.102546

Zusammenfassung

We prove that for any m ≥ 3, n ≫ m3, all secant varieties of the Segre-Veronese variety ℙm × ℙn have the expected dimension. This was already proved by Abo and Brambilla in the subabundant case, hence we focus on the superabundant case. We generalize an approach due to Brambilla and Ottaviani into a construction we call the inductant. With a combinatorial investigation of these constructions, the proof of non-defectivity reduces to checking a finite collection of base cases, which we verify using a computer-assisted proof.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Secant varieties, Segre-Veronese varieties, Non-defectivity

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ISO 690DOLEZALEK, Matej, Nikhil KEN, 2026. Secant varieties of Segre-Veronese varieties ℙm × ℙn embedded by 𝒪(1, 2) are non-defective for n ≫ m3, m ≥ 3. In: Journal of Symbolic Computation. Elsevier. 2026, 135, 102546. ISSN 0747-7171. eISSN 1095-855X. Verfügbar unter: doi: 10.1016/j.jsc.2025.102546
BibTex
@article{Dolezalek2026-07Secan-75638,
  title={Secant varieties of Segre-Veronese varieties ℙ<sup>m</sup> × ℙ<sup>n</sup> embedded by 𝒪(1, 2) are non-defective for n ≫ m<sup>3</sup>, m ≥ 3},
  year={2026},
  doi={10.1016/j.jsc.2025.102546},
  volume={135},
  issn={0747-7171},
  journal={Journal of Symbolic Computation},
  author={Dolezalek, Matej and Ken, Nikhil},
  note={Article Number: 102546}
}
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