On the Ulrichness of twisted syzygies and dual syzygies bundles

TL;DR

This paper classifies when twisted syzygies and dual syzygies bundles are Ulrich bundles on projective varieties with respect to certain polarizations, providing partial results for arbitrary polarizations.

Contribution

It offers a classification of Ulrich properties for twisted syzygy bundles on projective varieties under specific polarizations, advancing understanding in algebraic geometry.

Findings

Identifies conditions for Ulrich bundles among twisted syzygies.

Provides partial results for arbitrary polarizations.

Enhances classification of vector bundles on projective varieties.

Abstract

Given a projective variety $X$ and a very ample line bundle $\mathcal{L}$ on $X$, we classify for which $X$ and $\mathcal{L}$ the twisted syzygies and twisted dual syzygies bundles are Ulrich with respect to the polarizations $\mathcal{L}^a$. We obtain some partial results when considering an arbitrary polarization $H$.