On the rank index of projective curves of almost minimal degree

초록

In this article, we investigate the rank index of projective curves C subset of Pr of degree r +1 when C = pi(p)(C) for the standard rational normal curve C subset of Pr +1 and a point p E P (R) (+1) \ C-3 where C-k denotes the k-fold self-join of C. Here, the rank index of a closed subscheme X subset of P (R) is defined to be the least integer k such that the homogeneous ideal of X can be generated by quadratic polynomials of rank <= k. Our results show that the rank index of C is at most 4, and it is exactly equal to 3 when the projection center p is a coordinate point of Pr+1. We also investigate the case where p is an element of C-3 \ C-2. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

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