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2023-01-18

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cc by (c) Rosa M. Miró-Roig et al., 2023
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/220656

Ein–Lazarsfeld–Mustopa conjecture for the blow-up of a projective space

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https://doi.org/10.1007/s10231-023-01359-2

Abstract

We 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 $\left[M_L\right]$.

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Àlgebra commutativa, Superfícies algebraiques, Geometria algebraica, Varietats algebraiques

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Commutative algebra, Algebraic surfaces, Algebraic geometry, Algebraic varieties

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MIRÓ-ROIG, Rosa M. (Rosa Maria) and SALAT MOLTÓ, Martí. Ein–Lazarsfeld–Mustopa conjecture for the blow-up of a projective space. Annali di Matematica Pura ed Applicata. 2023. Vol. 203, num. 1, pags. 221-233. ISSN 0373-3114. [consulted: 17 of August of 2026]. Available at: https://hdl.handle.net/2445/220656

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