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2020 On the Hilbert Function of Intersections of a Hypersurface with General Reducible Curves
Edoardo Ballico
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Albanian J. Math. 14(1): 79-90 (2020). DOI: 10.51286/albjm/1608313767

Abstract

Let $W \subset \mathbb P^n, n \ge 3$, be a degree k hypersurface. Consider a "general" nodal union of $d$ lines $L_1, \dots L_d$ with $L_i \cap L_j \neq \emptyset$ if and only if $|i - j| \le 1$ (here called a degree $d$ bamboo). We study the Hilbert function of the set $Y \cap W$ with cardinality $k \deg(Y)$ and prove that it is the expected one (with a few classified exceptions $(n,k,d)$) when $W$ is either a quadric hypersurface of rank at least $2$ or $n = 3$ and $W$ is an integral cubic surface.

Funding Statement

The author was partially supported by MIUR and GNSAGA of INdAM (Italy).

Citation

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Edoardo Ballico. "On the Hilbert Function of Intersections of a Hypersurface with General Reducible Curves." Albanian J. Math. 14 (1) 79 - 90, 2020. https://doi.org/10.51286/albjm/1608313767

Information

Published: 2020
First available in Project Euclid: 18 December 2020

MathSciNet: MR4164626
Digital Object Identifier: 10.51286/albjm/1608313767

Subjects:
Primary: 14H50

Rights: Copyright © 2020 Research Institute of Science and Technology (RISAT)

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Vol.14 • No. 1 • 2020
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