Concomitants of Ternary Quartics and Vector-valued Siegel and Teichmüller Modular Forms of Genus Three

2019/08/12 by Cléry, Fabien, Faber, Carel, van der Geer, Gerard · 2 citations
#10D #11F46 #14H10 #14H45 #14J15 #14K10 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1908.04248

Abstract

We show how one can use the representation theory of ternary quartics to construct all vector-valued Siegel modular forms and Teichmüller modular forms of degree 3. The relation between the order of vanishing of a concomitant on the locus of double conics and the order of vanishing of the corresponding modular form on the hyperelliptic locus plays an important role. We also determine the connection between Teichmüller cusp forms on M_g and the middle cohomology of symplectic local systems on M_g. In genus 3, we make this explicit in a large number of cases.

Cited by

• Siegel modular forms arising from higher Chow cycles
• RNS superstring measure for genus 3

Related

• Siegel modular forms of degree three and the cohomology of local systems
• Siegel modular forms of degree two and three and invariant theory
• Siegel modular forms (mod p) and algebraic modular forms
• Siegel modular forms of genus 2 and level 2
• Quinary forms and paramodular forms