algebraic cone; monoid action; group action; orbit; action with unique fixed point; algebra automorphism; stable ideal; irreducible algebraic variety toric variety; Weil divisor; Cartier divisor; convexity; Picard number; polytope; polyhedron; sheaf cohomology; Hizrebruch-Jung continued fraction; Gröbner fan; McKay correspondence; Rees algebra; multiplier ideal; Hirzebruch-Riemann-Roch theorem; Chow ring; intersection cohomology; invariant theory; GKZ cone; secondary fan; spectral sequence 