algebraic cone; monoid action; group action; orbit; action with unique fixed point; algebra automorphism; stable ideal; irreducible algebraic variety very ample line bundle; positive line bundle; homogeneous Kähler manifold; blowing-up; Fermat hypersurface; holomorphic action of compact Lie group; representation ring; Grassmannian; twisted Dolbeault operator; Atiyah-Singer fixed point formula; representation ring of a compact Lie group 