On the coregularity of del Pezzo surfaces with du Val singularities
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910039321608192 |
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| author | Loginov, Konstantin Trepalin, Andrey |
| author_facet | Loginov, Konstantin Trepalin, Andrey |
| contents | We compute the coregularity of del Pezzo surfaces with du Val singularities. To this aim, we study the relation between del Pezzo surfaces of degree $1$ and elliptic fibrations. It turns out that del Pezzo surfaces with positive coregularity correspond to isotrivial elliptic fibrations with some special properties. We also prove results about coregularity of del Pezzo surfaces over non-algebraically closed fields of characteristic $0$. Our results confirm the expectation that "most" del Pezzo surfaces have coregularity $0$, while del Pezzo surfaces with positive coregularity enjoy some special properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03041 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the coregularity of del Pezzo surfaces with du Val singularities Loginov, Konstantin Trepalin, Andrey Algebraic Geometry 14J26 We compute the coregularity of del Pezzo surfaces with du Val singularities. To this aim, we study the relation between del Pezzo surfaces of degree $1$ and elliptic fibrations. It turns out that del Pezzo surfaces with positive coregularity correspond to isotrivial elliptic fibrations with some special properties. We also prove results about coregularity of del Pezzo surfaces over non-algebraically closed fields of characteristic $0$. Our results confirm the expectation that "most" del Pezzo surfaces have coregularity $0$, while del Pezzo surfaces with positive coregularity enjoy some special properties. |
| title | On the coregularity of del Pezzo surfaces with du Val singularities |
| topic | Algebraic Geometry 14J26 |
| url | https://arxiv.org/abs/2603.03041 |