IJPAM: Volume 88, No. 2 (2013)

POSTULATION OF CURVES CONTAINED IN
A UNION OF HYPERPLANES OF $\mathbb {P}^4$

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY


Abstract. Let $A\subset \mathbb {P}^4$ be a union of $m$ distinct hyperplanes. In this note for many $m, d$ we prove the existence of reduced, connected and nodal curves $C\subset A$ with $\deg (C) = d$, $p_a(C)=0$ and maximal rank, i.e. $h^0(A,\mathcal {I}_{C,A}(t))\cdot h^1(A,\mathcal {I}_{C,A}(t)) =0$ for all $t\in \mathbb {N}$.

Received: June 1, 2013

AMS Subject Classification: 14H50, 14N05

Key Words and Phrases: postulation, reducible curve, reducible hypersurface, Hilbert function

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DOI: 10.12732/ijpam.v88i2.3 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 88
Issue: 2