تقرير
A note on some moduli spaces of Ulrich Bundles
| العنوان: | A note on some moduli spaces of Ulrich Bundles |
|---|---|
| المؤلفون: | Fania, Maria Lucia, Flamini, Flaminio |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, Primary 14J30, 14J26, 14J60, 14C05, Secondary 14N30 |
| الوصف: | 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. Comment: 10 pages, accepted for publication. The authors would like to thank M. Aprodu, since this article came about as a result of some of his questions during the conference "Algebraic Geometry in L'Aquila", July 18-21, 2023, and the anonymous Referee for his/her advices and questions which have also improved the presentation |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2405.09374 |
| رقم الأكسشن: | edsarx.2405.09374 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |