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

@article{Clry2019ConcomitantsOT,
title={Concomitants of Ternary Quartics and Vector-valued Siegel and Teichm{\"u}ller Modular Forms of Genus Three},
author={F. Cl{\'e}ry and C. Faber and G. Geer},
journal={arXiv: Algebraic Geometry},
year={2019}
}

We show how one can use the representation theory of ternary quartics to construct all vector-valued Siegel modular forms and Teichmuller 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 Teichmuller cusp forms on \overline{M}_g and the middle cohomology of symplectic local… CONTINUE READING