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arXiv · 2402.07254

Vector bundles without intermediate cohomology and the trichotomy result

Giorgio Ottaviani
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Abstract

Horrocks proved in 1964 that vector bundles on $P^n$ without intermediate cohomology split as direct sum of line bundles. This result has been the starting point of a great research activity on other varieties, showing interesting connections with derived categories and other areas. We follow some paths into this fascinating story, which has classical roots. The story has a culmination with the trichotomy result (finite/tame/wild) for arithmetically Cohen Macaulay (ACM) varieties obtained by Faenzi and Pons-Llopis in 2021. This is an expanded version of the talk given at the conference "Homemade Algebraic Geometry" in July 2023 at Alcal\'a de Henares celebrating Enrique Arrondo's 60th birthday.

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Giorgio Ottaviani. 2024-02-11. Vector bundles without intermediate cohomology and the trichotomy result. https://arxiv.org/abs/2402.07254

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