Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 51, Number 3 (2011), 633-645.
On a theorem of Castelnuovo and applications to moduli
In this paper we prove a theorem stated by Castelnuovo which bounds the dimension of linear systems of plane curves in terms of two invariants, one of which is the genus of the curves in the system. This extends a previous result of Castelnuovo and Enriques. We classify linear systems whose dimension belongs to certain intervals which naturally arise from Castelnuovo’s theorem. Then we make an application to the following moduli problem: what is the maximum number of moduli of curves of geometric genus varying in a linear system on a surface? It turns out that, for , the answer is , and it is attained by trigonal canonical curves varying on a balanced rational normal scroll.
Kyoto J. Math., Volume 51, Number 3 (2011), 633-645.
First available in Project Euclid: 1 August 2011
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14C20: Divisors, linear systems, invertible sheaves
Secondary: 14J26: Rational and ruled surfaces
Castorena, Abel; Ciliberto, Ciro. On a theorem of Castelnuovo and applications to moduli. Kyoto J. Math. 51 (2011), no. 3, 633--645. doi:10.1215/21562261-1299909. https://projecteuclid.org/euclid.kjm/1312205241