On the rank index of some quadratic varieties

2022/06/17 by Hyunsuk Moon, Moon, Hyunsuk, Euisung Park +1 · 1 citation
Mathematics · Medicine · #14N25 #14Q10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Phytoestrogen effects and research #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2206.08586

openalex publication_date 2022/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Regarding the generating structure of the homogeneous ideal of a projective variety X ⊂ ℙ^r, we define the rank index of X to be the smallest integer k such that I(X) can be generated by quadratic polynomials of rank at most k. Recently it is shown that every Veronese embedding has rank index 3 if the base field has characteristic ≠ 2, 3. In this paper, we introduce some basic ways of how to calculate the rank index and find its values when X is some other classical projective varieties such as rational normal scrolls, del Pezzo varieties, Segre varieties and the Plücker embedding of the Grassmannian of lines.

Cited by

• Rank 3 Quadratic Generators of Veronese Embeddings: The Characteristic 3 Case

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