A note on some moduli spaces of Ulrich Bundles
Maria Lucia Fania, Flaminio Flamini

TL;DR
This paper proves that certain moduli spaces of Ulrich bundles on 3-fold scrolls over Hirzebruch surfaces are generically smooth, irreducible, and unirational, providing new insights into their geometric structure.
Contribution
It establishes the generic smoothness, irreducibility, and unirationality of specific moduli spaces of Ulrich bundles on 3-fold scrolls over Hirzebruch surfaces, extending previous results.
Findings
Moduli spaces are generically smooth and unirational.
Stronger results show irreducibility and smoothness for associated moduli spaces.
Ulrich bundles are parametrized on suitable 3-fold scrolls over Hirzebruch surfaces.
Abstract
We prove that the modular component , 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 and given Chern classes, on suitable -fold scrolls over Hirzebruch surfaces , which arise as tautological embeddings of projectivization of very-ample vector bundles on , is generically smooth and unirational. A stronger result holds for the suitable associated moduli space of vector bundles of rank and given Chern classes on , Ulrich w.r.t. the very ample polarization which turns out to be generically smooth, irreducible and unirational.
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Taxonomy
TopicsAdvanced Algebra and Geometry · advanced mathematical theories · Algebraic Geometry and Number Theory
