  We study Einstein manifolds admitting a transitive solvable Lie group of
isometries (solvmanifolds). It is conjectured that these exhaust the class of
noncompact homogeneous Einstein manifolds. J. Heber has showed that under
certain simple algebraic condition called standard (i.e. the orthogonal
complement of the derived algebra is abelian), Einstein solvmanifolds have many
remarkable structural and uniqueness properties. In this paper, we prove that
any Einstein solvmanifold is standard, by applying a stratification procedure
from geometric invariant theory due to F. Kirwan.
