2024/05/15 by Maria Lucia Fania, Fania, Maria Lucia, Flaminio Flamini +1
Mathematics · #14C05 #14J26 #14J60 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Primary 14J30 #Secondary 14N30 #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2405.09374
openalex publication_date 2024/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the modular component \mathcal M(r), constructed in the Main Theorem of a former paper of us (published in Adv. Math on 2024), paramatrizing (isomorphism classes of) Ulrich vector bundles of rank r and given Chern classes, on suitable 3-fold scrolls Xe over Hirzebruch surfaces \mathbbFe≥ 0, which arise as tautological embeddings of projectivization of very-ample vector bundles on \mathbbFe, is generically smooth and unirational. A stronger result holds for the suitable associated moduli space \mathcal M\mathbb Fe(r) of vector bundles of rank r and given Chern classes on \mathbbFe, Ulrich w.r.t. the very ample polarization c1(\mathcal Ee) = \mathcal O\mathbb Fe(3, be), which turns out to be generically smooth, irreducible and unirational.