On the rank index of some quadratic varieties
| Autor: | Moon, Hyunsuk, Park, Euisung |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Regarding the generating structure of the homogeneous ideal of a projective variety $X \subset \mathbb{P}^r$, 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 $\ne 2, 3$. 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 Pl\"{u}cker embedding of the Grassmannian of lines. Comment: 17 pages |
| Databáze: | arXiv |
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