On varieties with Ulrich twisted conormal bundles

Abstract

We study varieties X ⊂ P r X \subset \mathbb {P}^r such that N X ∗ ( k ) N_X^*(k) is an Ulrich vector bundle for some integer k k . We first prove that such an X X must be a curve. Then we give several examples of curves with N X ∗ ( k ) N_X^*(k) an Ulrich vector bundle.