On the projective normality of Ulrich bundles on some low-dimensional varieties

TL;DR

This paper investigates the projective normality of Ulrich bundles on low-dimensional varieties, focusing on curves, certain surfaces, and hypersurfaces, to understand their embedding properties.

Contribution

It provides new insights into the projective normality of Ulrich bundles on specific low-dimensional varieties, expanding understanding of their geometric properties.

Findings

Ulrich bundles on curves exhibit projective normality under certain conditions.

Surface cases with $q=p_g=0$ are analyzed for projective normality.

Hypersurfaces of dimensions 2 and 3 are studied for Ulrich bundle embeddings.

Abstract

We study the projective normality of the projective bundle of an Ulrich vector bundle embedded through the complete linear system of its tautological line bundle. The focus will be on Ulrich bundles defined over curves, surfaces with $q=p_g=0$ and hypersurfaces of dimension $2$ and $3.$