Annales Academię Scientiarum Fennicę
Mathematica
Volumen 37, 2012, 285-300
University of Southampton, School of Mathematics
Southampton SO17 1BJ, United Kingdom; zelaing 'at' googlemail.com
University of Southampton, School of Mathematics
Southampton SO17 1BJ, United Kingdom; ds 'at' maths.soton.ac.uk
Abstract. We search for Riemann surfaces whose automorphism groups act transitively on their Weierstrass points. One example is Klein's quartic. We find all hyperelliptic surfaces with this property, all surfaces with this property whose automorphism group is PSL(2,q), many Platonic surfaces and other examples including Fermat curves. Basically, we find that the transitivity property seems quite rare and that the surfaces we have found with this property are interesting for other reasons too.
2010 Mathematics Subject Classification: Primary 30F10, 14H55, 20B25.
Key words: Compact Riemann surfaces, Weierstrass points, Fuchsian groups, finite automorphism groups.
Reference to this article: Z. Laing and D. Singerman: Transitivity on Weierstrass points. Ann. Acad. Sci. Fenn. Math. 37 (2012), 285-300.
doi:10.5186/aasfm.2012.3711
Copyright © 2012 by Academia Scientiarum Fennica