Miró-Roig, Rosa M. (Rosa Maria)Salat Moltó, Martí2025-04-282025-04-282023-01-180373-3114https://hdl.handle.net/2445/220656We solve the Ein-Lazarsfeld-Mustopa conjecture for the blow up of a projective space along a linear subspace. More precisely, let $X$ be the blow up of $\mathbb{P}^n$ at a linear subspace and let $L$ be any ample line bundle on $X$. We show that the syzygy bundle $M_L$ defined as the kernel of the evalution map $H^0(X, L) \otimes \mathcal{O}_X \rightarrow L$ is $L$-stable. In the last part of this note we focus on the rigidness of $M_L$ to study the local shape of the moduli space around the point $\left[M_L\right]$.13 p.application/pdfengcc by (c) Rosa M. Miró-Roig et al., 2023http://creativecommons.org/licenses/by/3.0/es/Àlgebra commutativaSuperfícies algebraiquesGeometria algebraicaVarietats algebraiquesCommutative algebraAlgebraic surfacesAlgebraic geometryAlgebraic varietiesinfo:eu-repo/semantics/article7436422025-04-28info:eu-repo/semantics/openAccess