On the moduli space of simple sheaves on singular K3 surfaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912188551135232 |
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| author | Fantechi, Barbara Miró-Roig, Rosa M. |
| author_facet | Fantechi, Barbara Miró-Roig, Rosa M. |
| contents | Mukai proved that the moduli space of simple sheaves on a smooth projective K3 surface is symplectic, and in \cite{FM2} we gave two constructions allowing one to construct new locally closed Lagrangian/isotropic subspaces of the moduli from old ones. In this paper, we extend both Mukai's result and our construction to reduced projective K3 surfaces; for the former we need to restrict our attention to perfect sheaves. There are two key points where we cannot get a straightforward generalization. In each, we need to prove that a certain differential form on the moduli space of simple, perfect sheaves vanishes, and we introduce a smoothability condition to complete the proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00735 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the moduli space of simple sheaves on singular K3 surfaces Fantechi, Barbara Miró-Roig, Rosa M. Algebraic Geometry Mukai proved that the moduli space of simple sheaves on a smooth projective K3 surface is symplectic, and in \cite{FM2} we gave two constructions allowing one to construct new locally closed Lagrangian/isotropic subspaces of the moduli from old ones. In this paper, we extend both Mukai's result and our construction to reduced projective K3 surfaces; for the former we need to restrict our attention to perfect sheaves. There are two key points where we cannot get a straightforward generalization. In each, we need to prove that a certain differential form on the moduli space of simple, perfect sheaves vanishes, and we introduce a smoothability condition to complete the proof. |
| title | On the moduli space of simple sheaves on singular K3 surfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2403.00735 |