### Abstract

I show that on any smooth, projective ordinary curve of genus at least two and a projective embedding, there is a natural example of a stable Ulrich bundle for this embedding: namely the sheaf B
_{X}
^{1}
of locally exact differentials twisted by O
_{X}
(1) given by this embedding and in particular there exist ordinary varieties of any dimension which carry Ulrich bundles. In higher dimensions, assuming X is Frobenius split variety I show that B
_{X}
^{1}
is an ACM bundle and if X is also a Calabi–Yau variety and p>2 then B
_{X}
^{1}
is not a direct sum of line bundles. In particular I show that B
_{X}
^{1}
is an ACM bundle on any ordinary Calabi–Yau variety. I also prove a characterization of projective varieties with trivial canonical bundle such that B
_{X}
^{1}
is ACM (for some projective embedding datum): all such varieties are Frobenius split (with trivial canonical bundle).

Original language | English (US) |
---|---|

Pages (from-to) | 20-29 |

Number of pages | 10 |

Journal | Journal of Algebra |

Volume | 527 |

DOIs | |

State | Published - Jun 1 2019 |

### Keywords

- ACM bundles
- Calabi–Yau variety
- Frobenius split varieties
- Ordinary varieties
- Ulrich bundles

### ASJC Scopus subject areas

- Algebra and Number Theory