Lagrangian Subspaces of the Moduli Space of Simple Sheaves on K3 Surfaces
Let $X$ be a K3 surface and let $\operatorname{Spl}\left(r ; c_1, c_2\right)$ be the moduli space of simple sheaves on $X$ of fixed rank $r$ and Chern classes $c_1$ and $c_2$. Under suitable assumptions, to a pair ( $F, W$ ) (respectively, $(F, V)$ ) where $F \in \operatorname{Spl}\left(r ; c_1, c_2...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:dnet:ubarcelona__::b9a5f605340e5f9b81f562decd237078 |
| Acceso en línea: | https://hdl.handle.net/2445/228973 |
| Access Level: | acceso abierto |
| Palabra clave: | Espais topològics Superfícies algebraiques Homologia Geometria algebraica Topological spaces Algebraic surfaces Homology Algebraic geometry |
| Sumario: | Let $X$ be a K3 surface and let $\operatorname{Spl}\left(r ; c_1, c_2\right)$ be the moduli space of simple sheaves on $X$ of fixed rank $r$ and Chern classes $c_1$ and $c_2$. Under suitable assumptions, to a pair ( $F, W$ ) (respectively, $(F, V)$ ) where $F \in \operatorname{Spl}\left(r ; c_1, c_2\right)$ and $W \subset H^0(F)$ (resp. $V^* \subset H^1\left(F^*\right)$ ) is a vector subspace, we associate a simple syzygy bundle (resp. extension bundle) on $X$. We show that both syzygy bundles and extension bundles can be constructed in families and that the induced morphism to a different component of the moduli of simple sheaves is a locally closed embedding. We show that this construction associates with every Lagrangian (resp. isotropic) algebraic subspace of $\operatorname{Spl}\left(r ; c_1, c_2\right)$ an induced Lagrangian (resp. isotropic) algebraic subspace of a different component of the moduli of simple sheaves. |
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