Vanishing Hessian, wild forms and their border VSP

Huang, Hang; Michalek, Mateusz; Ventura, Emanuele

Vanishing Hessian, wild forms and their border VSP

Dateien

Huang_2-1uyhhc0ccww44.pdfGröße: 465.52 KBDownloads: 149

Datum

2020

Autor:innen

Huang, Hang

Michalek, Mateusz

Ventura, Emanuele

Open Access-Veröffentlichung

Open Access Hybrid

Sammlungen

Mathematik und Statistik

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Mathematische Annalen. Springer. 2020, 378(3-4), pp. 1505-1532. ISSN 0025-5831. eISSN 1432-1807. Available under: doi: 10.1007/s00208-020-02080-8

Zusammenfassung

Wild forms are homogeneous polynomials whose smoothable rank is strictly larger than their border rank. The discrepancy between these two ranks is caused by the difference between the limit of spans of a family of zero-dimensional schemes and the span of their flat limit. For concise forms of minimal border rank, we show that the condition of vanishing Hessian is equivalent to being wild. This is proven by making a detour through structure tensors of smoothable and Gorenstein algebras. The equivalence fails in the non-minimal border rank regime. We exhibit an infinite series of minimal border rank wild forms of every degree d≥3 as well as an infinite series of wild cubics. Inspired by recent work on border apolarity of Buczyńska and Buczyński, we study the border varieties of sums of powers VSP of these forms in the corresponding multigraded Hilbert schemes.

Fachgebiet (DDC)

510 Mathematik

Zitieren

ISO 690

HUANG, Hang, Mateusz MICHALEK, Emanuele VENTURA, 2020. Vanishing Hessian, wild forms and their border VSP. In: Mathematische Annalen. Springer. 2020, 378(3-4), pp. 1505-1532. ISSN 0025-5831. eISSN 1432-1807. Available under: doi: 10.1007/s00208-020-02080-8

BibTex

@article{Huang2020Vanis-52468,
  year={2020},
  doi={10.1007/s00208-020-02080-8},
  title={Vanishing Hessian, wild forms and their border VSP},
  number={3-4},
  volume={378},
  issn={0025-5831},
  journal={Mathematische Annalen},
  pages={1505--1532},
  author={Huang, Hang and Michalek, Mateusz and Ventura, Emanuele}
}

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