On some "sporadic" moduli spaces of Ulrich bundles on some 3-fold scrolls over $\mathbb{F}_0$
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915066805223424 |
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| author | Fania, Maria Lucia Flamini, Flaminio |
| author_facet | Fania, Maria Lucia Flamini, Flaminio |
| contents | We investigate on the existence of some "sporadic", rank-$r \geqslant 1$ Ulrich vector bundles on suitable $3$-fold scrolls $X$ over the Hirzebruch surface $\mathbb{F}_0$, which arise as tautological embeddings of projectivization of very-ample vector bundles on $\mathbb{F}_0$ that are uniform in the sense of Brosius and Aprodu--Brinzanescu. Such Ulrich bundles arise as deformations of ``iterative" extensions by means of "sporadic" Ulrich line bundles. We moreover explicitely describe irreducible components of the corresponding "sporadic" moduli spaces of rank $r \geqslant 1$ vector bundles which are Ulrich with respect to the tautological polarization on $X$. In some cases such irreducible components turn out to be a singleton, in some other cases such components are generically smooth, whose positive dimension has been computed and whose general point turns out to be a slope-stable vector bundle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12174 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On some "sporadic" moduli spaces of Ulrich bundles on some 3-fold scrolls over $\mathbb{F}_0$ Fania, Maria Lucia Flamini, Flaminio Algebraic Geometry 14J30, 14J26, 14J60, 14C05, 14N30 We investigate on the existence of some "sporadic", rank-$r \geqslant 1$ Ulrich vector bundles on suitable $3$-fold scrolls $X$ over the Hirzebruch surface $\mathbb{F}_0$, which arise as tautological embeddings of projectivization of very-ample vector bundles on $\mathbb{F}_0$ that are uniform in the sense of Brosius and Aprodu--Brinzanescu. Such Ulrich bundles arise as deformations of ``iterative" extensions by means of "sporadic" Ulrich line bundles. We moreover explicitely describe irreducible components of the corresponding "sporadic" moduli spaces of rank $r \geqslant 1$ vector bundles which are Ulrich with respect to the tautological polarization on $X$. In some cases such irreducible components turn out to be a singleton, in some other cases such components are generically smooth, whose positive dimension has been computed and whose general point turns out to be a slope-stable vector bundle. |
| title | On some "sporadic" moduli spaces of Ulrich bundles on some 3-fold scrolls over $\mathbb{F}_0$ |
| topic | Algebraic Geometry 14J30, 14J26, 14J60, 14C05, 14N30 |
| url | https://arxiv.org/abs/2412.12174 |