Exceptional points in the elliptic-hyperelliptic locus

Details Exceptional points in the elliptic-hyperelliptic locus Exceptional points in the elliptic-hyperelliptic locus

2007-03-15

arxiv.org/abs/math/0703473v2

Journal of Pure and Applied Algebra 212 (2008) 1415-1426

Mathematics

Algebraic Geometry

23 pages; shortened for publication

Scientific paper

An exceptional point in the moduli space of compact Riemann surfaces is a unique surface class whose full automorphism group acts with a triangular signature. A surface admitting a conformal involution with quotient an elliptic curve is called elliptic-hyperelliptic; one admitting an anticonformal involution is called symmetric. In this paper, we determine, up to topological conjugacy, the full group of conformal and anticonformal automorphisms of a symmetric exceptional point in the elliptic-hyperelliptic locus. We determine the number of ovals of any symmetry of such a surface. We show that while the elliptic-hyperelliptic locus can contain an arbitrarily large number of exceptional points, no more than four are symmetric.

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