Welcome to Group Actions on Curves project

Group Actions on Algebraic Curves GAAC

There is a variety of groups that can act on a Riemann surface/algebraic curve over \(\mathbb{C}\); the automorphism group, the mapping class group (here we might allow punctures) and if the curve is defined over \(\bar{\mathbb{Q}}\) the absolute Galois group \(\mathrm{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})\) is also acting on the curve. Understanding the above groups is a difficult problem and these actions provide information on both the curve and the group itself. For all the groups mentioned above, the action can often be understood in terms of linear representations, by allowing the group to act on vector spaces and modules related to the curve itself, as the (co)homology groups and section of holomorphic differentials.

Surveys on Automorphisms of Curves

• J. Antoniadis, A. Kontogeorgis Automorphisms of Curves
• A. Broughton, T. Shaska, and A. Wootton On automorphisms of algebraic curves

Greece 2.0 Basic Research Financing Action (Horizontal support of all Sciences) Sub-action 2 Funding Projects in Leading-Edge Sectors.

Mathematics Department of the University of Athens.

Previous Next