arXiv subjects
Publications and source records attributed to Daniela Moura Prata.
In this work we will prove results that ensure the simplicity and the exceptionality of vector bundles which are defined by the splitting of pure resolutions. We will call such objects syzygy bundles.
We prove three results on pure resolutions of vector bundles on projective spaces. First, we show that there are simple vector bundles of rank n on Pn with arbitrary homological dimension. We then analyze the pure resolutions given by the sheafification of the Koszul complex of a certain algebra and by the sheafification of the minimal free resolution of a compressed Gorenstein Artinian graded algebra, proving that their syzygies are simple vector bundles. Our main tool is a result originally established by Brambilla, for which we give an alternative proof using representations of quivers.