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arXiv · 1210.7835

Pure resolutions of vector bundles on complex projective spaces

Marcos Jardim·Daniela Moura Prata
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Abstract

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.

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Marcos Jardim, Daniela Moura Prata. 2012-10-29. Pure resolutions of vector bundles on complex projective spaces. https://arxiv.org/abs/1210.7835

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