Ulrich bundles on a general blow–up of the plane

We prove that on Xn, the plane blown–up at n general points, there are Ulrich line bundles with respect to a line bundle corresponding to curves of degree m passing simply through the n blown–up points, with m less than or equal to 2 times the square root of n 2, and such that the line bundle in question is very ample on Xn. We prove that the number of these Ulrich line bundles tends to infinity with n. We also prove the existence of slope–stable rank–r Ulrich vector bundles on Xn, for n > 2 and any r > 1 and we compute the dimensions of their moduli spaces. These computations imply that Xn is Ulrich wil