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

# metadata.dc.description.abstract[].value
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 $\left[M_L\right]$.

# metadata.dc.relation.ispartof[].value
Annali di Matematica Pura ed Applicata, 2023, vol. 203, num.1, p. 221-233

# metadata.dc.rights[].value
cc by (c) Rosa M. Miró-Roig et al., 2023

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

# metadata.dc.title[].value
Ein–Lazarsfeld–Mustopa conjecture for the blow-up of a projective space