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Article Dans Une Revue Commentarii Mathematici Helvetici Année : 2022

Ulrich bundles on cubic fourfolds

Résumé

We show the existence of rank 6 Ulrich bundles on a smooth cubic fourfold. First, we construct a simple sheaf E\mathcal EE of rank 6 as an elementary modification of an ACM bundle of rank 6 on a smooth cubic fourfold. Such an E\mathcal EE appears as an extension of two Lehn–Lehn–Sorger–van Straten sheaves. Then we prove that a general deformation of E(1)\mathcal E(1)E(1) becomes Ulrich. In particular, this says that general cubic fourfolds have Ulrich complexity 6.

Dates et versions

hal-03951392 , version 1 (23-01-2023)

Identifiants

Citer

Daniele Faenzi, Yeongrak Kim. Ulrich bundles on cubic fourfolds. Commentarii Mathematici Helvetici, 2022, 97 (4), pp.691-728. ⟨10.4171/CMH/546⟩. ⟨hal-03951392⟩
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