On the $X$-rank of a curve $X\subset \mathbb {P}^n$: an extremal case
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- by E. Ballico PDF
- Proc. Amer. Math. Soc. 141 (2013), 1211-1213 Request permission
Abstract:
Let $X\subset \mathbb {P}^n$, $n \ge 3$, be an integral and non-degenerate curve. For any $P\in \mathbb {P}^n$ the $X$-rank $r_X(P)$ of $P$ is the minimal cardinality of a set $S\subset Y$ such that $P$ is in the linear span of $S$. Landsberg and Teitler proved that $r_X(P) \le n$ for any $X$ and any $P$. Here we classify the pairs $(X,Q)$, $Q\in X_{reg}$, such that all points of the tangent line $T_QX$ (except $Q$) have $X$-rank $n$: $X \cong \mathbb {P}^1$ and $T_QX$ has order of contact $\deg (X) +2-n$ with $X$ at $Q$.References
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Additional Information
- E. Ballico
- Affiliation: Department of Mathematics, University of Trento, 38123 Povo (TN), Italy
- MR Author ID: 30125
- Email: ballico@science.unitn.it
- Received by editor(s): June 25, 2011
- Received by editor(s) in revised form: August 18, 2011
- Published electronically: August 29, 2012
- Additional Notes: The author was partially supported by MIUR and GNSAGA of INdAM (Italy).
- Communicated by: Irena Peeva
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 1211-1213
- MSC (2010): Primary 14H99, 14N05
- DOI: https://doi.org/10.1090/S0002-9939-2012-11406-6
- MathSciNet review: 3008868