IJPAM: Volume 48, No. 2 (2008)

BINARY CURVES AND LADDERS WITH
GOOD POSTULATION IN $\mathbb {P}^3$

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.A genus $g \ge 2$ binary curve is a nodal curve $X = D_1\cup D_2$ such that $D_1\cong D_2 \cong \mathbb {P}^1$ and $\sharp (D_1\cap D_2) = g+1$. A ladder of genus $g$ is a nodal curve $X = D_1\cup D_2\cup E_1\cup \cdots \cup
E_{g+1}$ such that $D_j\cong E_i
\cong
\mathbb {P}^1$ and $\sharp (D_j\cap E_i)=1$ for all $i, j$, $D_1\cap D_2=E_h\cap E_k = \emptyset$ for all $h \ne k$. Here we prove the existence of many embeddings of a general genus $g$ binary curve (resp. ladder) in $\mathbb {P}^3$ and with good postulation (resp. good postulation and in which each $E_i$ is embedded as a line).

Received: August 29, 2008

AMS Subject Classification: 14H50, 14H10, 14H20

Key Words and Phrases: reducible curve, postulation, binary curve, stable curve

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 48
Issue: 2