**Corollary:** If X is smooth then G has either no fixed point or at least two of them.

This is an algebraic analogue of (much deeper) results of Conner-Floyd, Atiyah-Bott and others in the topological category.}, author = {Assadi, Amir and Barlow, Rebecca and Knop, Friedrich}, doi = {10.1007/BF02571787}, faupublication = {no}, journal = {Mathematische Zeitschrift}, pages = {129-136}, peerreviewed = {Yes}, title = {{Abelian} group actions on algebraic varieties with one fixed point}, volume = {210}, year = {1992} }