For curves, surfaces with q=pg=0, and hypersurfaces of dimension 2 or 3, the paper gives criteria for when Ulrich bundles are projectively normal, with a likely error in the hypersurface determinant computation.
Akahori, Remarks on normal generation of line bundles on algebraic cu rves, Abh
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On the projective normality of Ulrich bundles on some low-dimensional varieties
For curves, surfaces with q=pg=0, and hypersurfaces of dimension 2 or 3, the paper gives criteria for when Ulrich bundles are projectively normal, with a likely error in the hypersurface determinant computation.