An Ulrich line bundle on a smooth projective variety 
of dimension 
, relative to a Cartier divisor 
whose associated line bundle 
is very ample, is
a line bundle 
satisfying
 |
for every 
and 
.
The notation denotes sheaf cohomology, and 
is the tensor
product of 
with 
.
The very ample divisor,
which specifies the projective embedding, is part of the definition (Beauville 2018).
On a complex Enriques surface with no smooth rational curves, Borisov and Nuer (2018) related
such bundles to divisor classes 
: the line bundle 
is Ulrich iff 
. Wang and Yi (2026) proved the Borisov-Nuer
conjecture and thereby established the existence of an Ulrich line bundle for
every choice of a very ample divisor 
of an unnodal Enriques
surface.
