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Lagrangian Subspaces of the Moduli Space of Simple Sheaves on K3 Surfaces

# metadata.dc.description.abstract[].value
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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Mediterranean Journal of Mathematics, 2025, vol. 22, num.21

# metadata.dc.rights[].value
cc by (c) Fantechi, Barbara et al., 2025

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Lagrangian Subspaces of the Moduli Space of Simple Sheaves on K3 Surfaces