Abstract
In this paper, we consider the problem of determining the Hilbert function of a general union \({X\subset \mathbb{P}^n}\) of an m-point mP and a general smooth rational curve of degree s. If \({n\geq 4}\), then X has the expected Hilbert function, i.e., X has maximal rank. If n = 3, then there are exceptional cases (if \({3\leq s\leq m}\)). We conjecture that these are the only exceptional cases and we prove this conjecture in several cases (e.g., if \({s\gg m}\)).
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The author was partially supported by MIUR and GNSAGA of INdAM (Italy).
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Ballico, E. Postulation of a General Union of an m-Point and a General Smooth Rational Curve. Mediterr. J. Math. 12, 281–300 (2015). https://doi.org/10.1007/s00009-014-0418-x
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DOI: https://doi.org/10.1007/s00009-014-0418-x