The locus of curves with prescribed automorphism group (Communications in Arithmetic Fundamental Groups)

By Kay Magaard, Tanush Shaska, Sergey V. Shpectorov, H. Voelklein. 2002

108 citations recorded by the source corpus.

Let G be a finite group, and $g \geq 2$. We study the locus of genus g curves that admit a G-action of given type, and inclusions between such loci. We use this to study the locus of genus g curves with prescribed automorphism group G. We completely classify these loci for g=3 (including equations for the corresponding curves), and for $g \leq 10$ we classify those loci corresponding to "large" G.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/130d0c55f3ddad4438cc7d1ba8d2767e3a34eb90

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

1. Christophe Ritzenthaler
2. Reynald Lercier
3. Jennifer Paulhus

In Geometry and Topology

1. Christophe Ritzenthaler
2. Reynald Lercier
3. Jennifer Paulhus

In Mathematical Physics

1. Christophe Ritzenthaler
2. Reynald Lercier
3. Jennifer Paulhus

Citations in the corpus

• Hyperelliptic curves and their invariants: geometric, arithmetic and algorithmic aspects (2011, methodology): “• In both references [37] and [27], case 11 of Fig.”
• Decomposing Jacobians of curves with extra automorphisms (2008, methodology): “For genus greater than 6, our computations produced no groups G from the data in [14] such that there is a g × g matrix ring in the decomposition of Q[G].”