  We introduce and study vertex cover algebras of weighted simplicial
complexes. These algebras are special classes of symbolic Rees algebras. We
show that symbolic Rees algebras of monomial ideals are finitely generated and
that such an algebra is normal and Cohen-Macaulay if the monomial ideal is
squarefree. For a simple graph, the vertex cover algebra is generated by
elements of degree 2, and it is standard graded if and only if the graph is
bipartite. We also give a general upper bound for the maximal degree of the
generators of vertex cover algebras.
