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arXiv · 2502.18360

Modular vector bundles on hyperk\"ahler manifolds of Debarre-Voisin type

Alessandro Frassineti·Federico Tufo
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Abstract

Let X be a very general Debarre--Voisin fourfold. In this article, we prove that all the Schur functors of the restriction of the quotient bundle of Gr(6,10) to X are modular and polystable vector bundles. We also show that the atomic bundles among them are exactly the symmetric powers of the restriction of the quotient bundle. Moreover, we compute the Ext}-groups of different modular vector bundles on X, and we find examples with non-trivial dimensional first Ext}-group.

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Alessandro Frassineti, Federico Tufo. 2025-02-25. Modular vector bundles on hyperk\"ahler manifolds of Debarre-Voisin type. https://arxiv.org/abs/2502.18360

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