Examples of surfaces which are Ulrich-wild

TL;DR

This paper provides examples of algebraic surfaces that support large families of non-isomorphic, indecomposable Ulrich bundles, demonstrating the complexity and richness of their Ulrich bundle moduli.

Contribution

It introduces specific surfaces that are Ulrich-wild, supporting arbitrarily large families of Ulrich bundles, expanding understanding of Ulrich bundle diversity.

Findings

Existence of surfaces supporting arbitrarily large families of Ulrich bundles

Construction of examples of Ulrich-wild surfaces

Demonstration of the complexity of Ulrich bundle moduli on these surfaces

Abstract

We give examples of surfaces which are Ulrich-wild, i.e. that support families of dimension $p$ of pairwise non-isomorphic, indecomposable, Ulrich bundles for arbitrary large $p$.