A note on some moduli spaces of Ulrich Bundles
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909204063715328 |
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| author | Fania, Maria Lucia Flamini, Flaminio |
| author_facet | Fania, Maria Lucia Flamini, Flaminio |
| contents | 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 $X_e$ over Hirzebruch surfaces $\mathbb{F}_{e\geq 0}$, which arise as tautological embeddings of projectivization of very-ample vector bundles on $\mathbb{F}_e$, is generically smooth and unirational. A stronger result holds for the suitable associated moduli space $\mathcal M_{\mathbb F_e}(r)$ of vector bundles of rank $r$ and given Chern classes on $\mathbb{F}_e$, Ulrich w.r.t. the very ample polarization $c_1({\mathcal E}_e) = \mathcal O_{\mathbb F_e}(3, b_e),$ which turns out to be generically smooth, irreducible and unirational. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09374 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on some moduli spaces of Ulrich Bundles Fania, Maria Lucia Flamini, Flaminio Algebraic Geometry Primary 14J30, 14J26, 14J60, 14C05, Secondary 14N30 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 $X_e$ over Hirzebruch surfaces $\mathbb{F}_{e\geq 0}$, which arise as tautological embeddings of projectivization of very-ample vector bundles on $\mathbb{F}_e$, is generically smooth and unirational. A stronger result holds for the suitable associated moduli space $\mathcal M_{\mathbb F_e}(r)$ of vector bundles of rank $r$ and given Chern classes on $\mathbb{F}_e$, Ulrich w.r.t. the very ample polarization $c_1({\mathcal E}_e) = \mathcal O_{\mathbb F_e}(3, b_e),$ which turns out to be generically smooth, irreducible and unirational. |
| title | A note on some moduli spaces of Ulrich Bundles |
| topic | Algebraic Geometry Primary 14J30, 14J26, 14J60, 14C05, Secondary 14N30 |
| url | https://arxiv.org/abs/2405.09374 |