IJPAM: Volume 25, No. 3 (2005)

FAMILIES OF $k$-GONAL CURVES WITH
CERTAIN SCROLLAR INVARIANTS, II

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


Abstract.Fix integers $g \ge 4$, $k \ge 4$ and $m \ge 2$. Let $\mathcal {S}(g,k,m)$ denote the set of all pairs $(X,R)$, where $X$ is a smooth and connected curve of genus $g$, $R\in \mbox{Pic} ^k(X)$, $R$ is spanned, $h^0(X,R^{\otimes (m-1)})=m$, $h^0(X,R^{\otimes m}) \ge m+2$ and the morphism $\psi$ induced by $H^0(X,R^{\otimes m})$ is birational. Set $\mathcal {S}(g,k,m,=):= \{(X,R)\in \mathcal {S}(g,k,m): h^0(X,R^{\otimes m}) = m+2\}$. Here we give (for many $g,k,m$) of several scrollar invariants of a general $(X,R)\in \mathcal {S}(g,k,m,=)$.

Received: September 30, 2005

AMS Subject Classification: 14H45, 14H50, 14H51

Key Words and Phrases: scrollar invariant, $k$-gonal curve, Hirzebruch surface

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 25
Issue: 3