## Kodai Mathematical Journal

### On the Castelnuovo-Severi inequality for Riemann surfaces

Robert D. M. Accola

#### Abstract

Some consequences of equality in the Castelnuovo-Severi inequality are discussed. In particular, it is shown that if a Riemann surface of genus ten, W10, admits four coverings of tori, each in three sheets, then W10 admits an elementary abelian group of order 27. By previous work this last result is then characterized by the vanishing of certain thetanulls. An elementary discussion of the direct product of monodromy groups is an essential part of the proofs.

#### Article information

Source
Kodai Math. J., Volume 29, Number 2 (2006), 299-317.

Dates
First available in Project Euclid: 3 July 2006

https://projecteuclid.org/euclid.kmj/1151936443

Digital Object Identifier
doi:10.2996/kmj/1151936443

Mathematical Reviews number (MathSciNet)
MR2247438

Zentralblatt MATH identifier
1116.14019

#### Citation

Accola, Robert D. M. On the Castelnuovo-Severi inequality for Riemann surfaces. Kodai Math. J. 29 (2006), no. 2, 299--317. doi:10.2996/kmj/1151936443. https://projecteuclid.org/euclid.kmj/1151936443