algebraic cone; monoid action; group action; orbit; action with unique fixed point; algebra automorphism; stable ideal; irreducible algebraic variety Siegel modular forms; cubic hypersurfaces; zero set of the Fermat ideal; Schottky modular form; Gauss map on the theta divisor; principally polarized Abelian variety; theta function; Siegel modular group; Jacobian of a generic curve; Fermat cubic; cubic forms 