Algebraic Curves and Modular Forms of Low Genus
Modular forms play an important role in number theory and algebraic geometry. Elliptic
modular forms are well-known, but Siegel modular forms of higher genus are much harder
to construct. For genus 2 and 3 modular forms are intimately connected with the moduli of
curves of genus 2 and 3. We give an explicit way to describe such 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.