Nonemptiness of Severi varieties on Enriques surfaces
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866909145351847936 |
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| author | Ciliberto, Ciro Dedieu, Thomas Galati, Concettina Knutsen, Andreas Leopold |
| author_facet | Ciliberto, Ciro Dedieu, Thomas Galati, Concettina Knutsen, Andreas Leopold |
| contents | Let $(S,L)$ be a general polarized Enriques surface, with $L$ not numerically 2-divisible. We prove the existence of regular components of all Severi varieties of irreducible $δ$-nodal curves in the linear system $|L|$, with $0\leq δ\leq p_a(L)-1$. This solves a classical open problem and gives a positive answer to a recent conjecture of Pandharipande--Schmitt, under the additional condition of non-2-divisibility. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_10735 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Nonemptiness of Severi varieties on Enriques surfaces Ciliberto, Ciro Dedieu, Thomas Galati, Concettina Knutsen, Andreas Leopold Algebraic Geometry Let $(S,L)$ be a general polarized Enriques surface, with $L$ not numerically 2-divisible. We prove the existence of regular components of all Severi varieties of irreducible $δ$-nodal curves in the linear system $|L|$, with $0\leq δ\leq p_a(L)-1$. This solves a classical open problem and gives a positive answer to a recent conjecture of Pandharipande--Schmitt, under the additional condition of non-2-divisibility. |
| title | Nonemptiness of Severi varieties on Enriques surfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2109.10735 |