On the existence of Ulrich bundles on blown-up varieties at a point

Abstract

The objective is to show the construction of an Ulrich vector bundle on the blowing-up $\widetilde X$ of a nonsingular projective variety $X$ at a closed point, where the original variety is embedded by a very ample divisor $H$ and carries an Ulrich vector bundle. In order to achieve this result, we aim to find a suitable very ample divisor on $\widetilde X$, which is dependent on $H$. At the end, we take into consideration some applications to surfaces with regards to minimal models and their Kodaira dimension.