2023/03/01 by Maria Lucia Fania, Fania, Maria Lucia, Flaminio Flamini +1
Mathematics · #14C05 #14J27 #14J60 #14N25 #14N30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 14J30 #Secondary 14M07
paper · pdf · doi:10.48550/arxiv.2303.00676
openalex publication_date 2023/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the existence of Ulrich vector bundles on suitable 3-fold scrolls Xe over Hirzebruch surfaces \mathbbFe, for any integer e \geqslant 0, which arise as tautological embeddings of projectivization of very-ample vector bundles on \mathbbFe that are uniform in the sense of Brosius and Aprodu--Brinzanescu. We explicitely describe components of moduli spaces of rank r \geqslant 1 vector bundles which are Ulrich with respect to the tautological polarization on Xe and whose general point is a slope-stable, indecomposable vector bundle. We moreover determine the dimension of such components, proving also that they are generically smooth. As a direct consequence of these facts, we also compute the Ulrich complexity of any such Xe and give an effective proof of the fact that these Xe's turn out to be geometrically Ulrich wild. At last, the machinery developed for 3--fold scrolls Xe allows us to deduce Ulrichness results on rank r \geqslant 1 vector bundles on \mathbbFe, for any e \geqslant 0, with respect to a naturally associated (very ample) polarization.