IJPAM: Volume 55, No. 2 (2009)

PROPERTY $N_p$ FOR LOW DEGREE
NON-SPECIAL EMBEDDINGS OF GENERAL CURVES

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


Abstract.Fix integers $g, r$ such that $g \ge 7$ and $g - \lfloor (g-3)/2\rfloor \le r \le g-2$. Set $d:= g+r$ and $p:=\lfloor (g-3)/2\rfloor -(g-1-r)$. Let $C$ be a general smooth curve of genus $g$ and $L$ a general element of $\mbox{Pic}^d(C)$. Here we prove that $L$ has property $N_p$, i.e. the Koszul cohomology groups $K_{i,j}(C,L)$ vanish for all integers $i, j$ such that $0 \le i \le p$ and $j\ge 2$.

Received: July 27, 2009

AMS Subject Classification: 14H50, 13D02

Key Words and Phrases: Koszul cohomology, property $N_p$, curves with general moduli

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 55
Issue: 2