On varieties with Ulrich twisted conormal bundles

Abstract

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

v2: we specified the results that hold in characteristic zero and the ones holding in any characteristic. Thanks to crucial remarks of anonymous referee, we improved Theorem 3(ii) to $g\ge 3$ and we rewrote completely and shortened section 8 by using interpolation techniques