Ulrich bundles on ruled surfaces
  In this short note, we study the existence problem for Ulrich bundles on ruled surfaces, focusing our attention on the smallest possible rank. We show that existence of Ulrich line bundles occurs if and only if the coefficient $\alpha$ of the minimal section in the numerical class of the polarization equals one. For other polarizations, we prove the existence of rank two Ulrich bundles. 
Marian Aprodu, Laura Costa, Rosa Maria Miro-Roig
math.AG