JOURNAL ARTICLE

Steiner representations of hypersurfaces.

  • Published In: International Journal of Mathematics, 2025, v. 36, n. 4. P. 1 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Antonelli, Vincenzo; Casnati, Gianfranco 3 of 3

Abstract

Let X ⊆ ℙ n + 1 be an integral hypersurface of degree d. We show that each locally Cohen–Macaulay instanton sheaf ℰ on X with respect to X ⊗ ℙ n + 1 (1) in the sense of [V. Antonelli and G. Casnati, Instanton sheaves on projective schemes, J. Pure Appl. Algebra 227 (2023) 107246, Definition 1.3] yields the existence of Steiner bundles and ℱ on ℙ n + 1 of the same rank r and a morphism φ : (− 1) → ℱ ∨ such that the form defining X to the power rk (ℰ) is exactly det (φ). We inspect several examples for low values of d , n and rk (ℰ). In particular, we show that the form defining a smooth integral surface in ℙ 3 is the pfaffian of some skew-symmetric morphism φ : ℱ (− 1) → ℱ ∨ , where ℱ is a suitable Steiner bundle on ℙ 3 of sufficiently large even rank. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:International Journal of Mathematics. 2025/03, Vol. 36, Issue 4, p1
  • Document Type:Article
  • Subject Area:Biography
  • Publication Date:2025
  • ISSN:0129-167X
  • DOI:10.1142/S0129167X24500812
  • Accession Number:182611722
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