  An Ulrich sheaf on an embedded projective variety is a normalized
arithmetically Cohen-Macaulay sheaf with the maximum possible number of
independent sections. Ulrich sheaves are important in the theory of Chow forms,
Boij-Soderberg theory, generalized Clifford algebras, and for an approach to
Lech's conjecture in commutative algebra. In this note, we give a reduction of
the construction of Ulrich sheaves on a projective variety X to the
construction of an Ulrich sheaf for a finite map of curves, which is in turn
equivalent to a higher-rank Brill-Noether problem for any of a certain class of
curves on X. Then we show that existence of an Ulrich sheaf for a finite map of
curves implies sharp numerical constraints involving the degree of the map and
the ramification divisor.
