IJPAM: Volume 54, No. 3 (2009)

MAXIMAL RANK IN $\mathbb {P}^r$

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: [email protected]

Abstract.Fix integers $r, b$ such that $r \ge 3$ and $b>0$. Here for most integers $d, g$ such that $(r-2)g/(r-1) < d < g+r-b$ we prove the existence of a nodal, smoothable and connected $C\subset \mathbb {P}^r$ with maximal rank such that $\deg (C)=d$, $p_a(C)=g$, $h^1(C,N_C)=0$, $h^0(C,\mathcal {O}_C(1)) = r+1+b$.

Received: May 25, 2009

AMS Subject Classification: 14H50

Key Words and Phrases: postulation, curve in $\mathbb {P}^n$, maximal rank, reducible curve

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 54
Issue: 3