We prove that the modular component 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 Fe≥0, which arise as tautological embeddings of projectivization of very-ample vector bundles on Fe, is generically smooth and unirational. A stronger result holds for the suitable associated moduli space MFe(r) of vector bundles of rank r and given Chern classes on Fe, Ulrich w.r.t. the very ample polarization c1(Ee)=OFe(3,be), which turns out to be generically smooth, irreducible and unirational.

Flamini, F., Fania Maria, L. (2024). A note on some moduli spaces of Ulrich bundles. RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO [10.1007/s12215-024-01068-6].

A note on some moduli spaces of Ulrich bundles

Flamini Flaminio
;
2024-06-10

Abstract

We prove that the modular component 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 Fe≥0, which arise as tautological embeddings of projectivization of very-ample vector bundles on Fe, is generically smooth and unirational. A stronger result holds for the suitable associated moduli space MFe(r) of vector bundles of rank r and given Chern classes on Fe, Ulrich w.r.t. the very ample polarization c1(Ee)=OFe(3,be), which turns out to be generically smooth, irreducible and unirational.
10-giu-2024
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03
English
Con Impact Factor ISI
Ulrich Bundles
open access at https://link.springer.com/article/10.1007/s12215-024-01068-6
https://link.springer.com/article/10.1007/s12215-024-01068-6
Flamini, F., Fania Maria, L. (2024). A note on some moduli spaces of Ulrich bundles. RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO [10.1007/s12215-024-01068-6].
Flamini, F; Fania Maria, L
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/363028
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