On the connectedness of some degeneracy loci and of Ulrich subvarieties
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915644618833920 |
|---|---|
| author | Buttinelli, Valerio Lopez, Angelo Felice Vacca, Roberto |
| author_facet | Buttinelli, Valerio Lopez, Angelo Felice Vacca, Roberto |
| contents | We study connectedness of degeneracy loci $D_{r-k}(φ)$ of morphisms $φ: {\mathcal O}_X^{\oplus (r+1-k)} \to \mathcal E$, where $\mathcal E$ is a rank $r$ globally generated bundle on a smooth $n$-dimensional variety $X$ and $k \le 3$. For $k \le 2$ we give a characterization of connectedness in terms of vanishing of Chern classes. Moreover we prove that they are connected, for $k \le \min\{2, r-1,n-1\}$, if $\mathcal E$ is V-big. In the case of Ulrich bundles more precise results are given, both in general and in the case of surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_00228 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the connectedness of some degeneracy loci and of Ulrich subvarieties Buttinelli, Valerio Lopez, Angelo Felice Vacca, Roberto Algebraic Geometry We study connectedness of degeneracy loci $D_{r-k}(φ)$ of morphisms $φ: {\mathcal O}_X^{\oplus (r+1-k)} \to \mathcal E$, where $\mathcal E$ is a rank $r$ globally generated bundle on a smooth $n$-dimensional variety $X$ and $k \le 3$. For $k \le 2$ we give a characterization of connectedness in terms of vanishing of Chern classes. Moreover we prove that they are connected, for $k \le \min\{2, r-1,n-1\}$, if $\mathcal E$ is V-big. In the case of Ulrich bundles more precise results are given, both in general and in the case of surfaces. |
| title | On the connectedness of some degeneracy loci and of Ulrich subvarieties |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2512.00228 |