The best-known modular forms are elliptic modular forms;
a natural generalization are vector-valued Siegel modular forms of genus g.
For genus 2 and 3 these modular forms are intimately connected with
the moduli of curves of genus 2 and 3. We give an explicit way to
describe such vector-valued modular forms for genus 2 and 3
using invariant theory and give some applications.
This is based on joint work with Fabien Clery and Carel Faber.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/246