Hyperkähler fourfolds of Kummer type: modular sheaves and projective models

Apparaît dans la collection : Géométrie algébrique en l'honneur de Claire Voisin

We describe a construction of stable rank 4 vector bundles on a general fourfold of Kummer type with polarization of divisibility 2 and square congruent to -6 modulo 16. These vector bundles are fixed by any automorphism acting trivially on 2 cohomology. We discuss the relevance of this property in the quest for an explicit locally complete family of polarized fourfolds of Kummer type.