turkmath.org

A vector bundle $\mathcal{E}$ on a projective variety $X$ in $\mathbb{P}^N$ is Ulrich if $H^∗(X,E(−k))$ vanishes for $1 ≤k ≤\dim(X)$. It has been conjectured by Eisenbud and Schreyer that every projective variety carries an Ulrich bundle. Even though this conjecture has not been proved or disproved, another interesting question is worth considering: classify projective varieties as Ulrich finite, tame or wild type with respect to families of Ulrich bundles that they support. In this talk, we will show that this trichotomy is exhaustive for certain del Pezzo surfaces with any given polarization. This talk is based on a joint work with Emre Coşkun.