On the classification of polarized surfaces with weakly Ulrich or initialized aCM tangent bundles
Year: 2026
Type: preprint
Abstract: Counterexamples to the Eisenbud-Schreyer conjecture on the existence of Ulrich bundles have appeared recently (see Anghel [A1] and the third author [Lo]). As weakly Ulrich bundles are a useful generalization of Ulrich ones, in this paper, we classify smooth surfaces $S\subseteq \mathbb P^N$ with weakly Ulrich tangent bundle. They are Del-Pezzo surfaces of degree at least 5 and we classify the possible embeddings. An interesting feature is the appearance of two infinite series of polarizations, which is quite different from the Ulrich case [BMPT, LR]. We also achieve the classification of surfaces with initialized aCM tangent bundles and, as a consequence, of surfaces with almost Ulrich tangent bundles.
Source: arXiv (Cornell University)
Institution: Roma Tre University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220686330