We investigate the existence of Ulrich vector bundles on suitable 3-fold scrolls Xe over Hirzebruch surfaces Fe, for any e⩾0, which arise as tautological embedding of projectivization of very-ample vector bundles on Fe which are uniform in the sense of Brosius and Aprodu--Brinzanescu (cf. [8] and [3], respectively, in Bibliography). We explicitely describe components of moduli spaces of rank r⩾1 Ulrich vector bundles whose general point is a slope-stable, indecomposable vector bundle. We moreover determine the dimension of such components as well as we prove 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 such Xe's turn out to be geometrically Ulrich wild.

Flamini, F., Fania Maria, L. (2024). Ulrich bundles on some threefold scrolls over F_e. ADVANCES IN MATHEMATICS, 436 [10.1016/j.aim.2023.109409].

Ulrich bundles on some threefold scrolls over F_e

Flamini Flaminio
Membro del Collaboration Group
;
2024-01-01

Abstract

We investigate the existence of Ulrich vector bundles on suitable 3-fold scrolls Xe over Hirzebruch surfaces Fe, for any e⩾0, which arise as tautological embedding of projectivization of very-ample vector bundles on Fe which are uniform in the sense of Brosius and Aprodu--Brinzanescu (cf. [8] and [3], respectively, in Bibliography). We explicitely describe components of moduli spaces of rank r⩾1 Ulrich vector bundles whose general point is a slope-stable, indecomposable vector bundle. We moreover determine the dimension of such components as well as we prove 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 such Xe's turn out to be geometrically Ulrich wild.
1-gen-2024
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - GEOMETRIA
English
Con Impact Factor ISI
Urlich vector bundles; 3folds; ruled varieties
publication open access
Flamini, F., Fania Maria, L. (2024). Ulrich bundles on some threefold scrolls over F_e. ADVANCES IN MATHEMATICS, 436 [10.1016/j.aim.2023.109409].
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/2108/317238
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