IJPAM: Volume 95, No. 2 (2014)

POSTULATION OF GENUS 1 PROJECTIVE CURVES
WITH LINES AS THEIR IRREDUCIBLE COMPONENTS

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


Abstract. Fix lines $L_1,\dots ,L_d\subset \mathbb {P}^n$, $d\ge 3$, such that $A:= L_1\cup \cdots \cup L_d$ is a nodal curve of degree $d$ and $L_i\cap L_j\ne \emptyset$ if and only if either $\vert i-j\vert\le 1$ or $(i,j) \in \{(1,d),(d,1)\}$. We say that $A$ is a genus 1 loop of degree $d$. We prove that general genus 1 loops of degree $d$ have maximal rank, i.e. good postulations, if either $n\ge 4$ or $n=3$ and most $d$. We also study the postulation of general disjoint unions of such curves.

Received: April 21, 2014

AMS Subject Classification: 14N05, 15A69

Key Words and Phrases: unions of lines, genus one, reducible curve, postulation, Hilbert function

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DOI: 10.12732/ijpam.v95i2.9 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: 2014
Volume: 95
Issue: 2
Pages: 233 - 243


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