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RIGID STABLE VECTOR BUNDLES ON HYPERKÄHLER VARIETIES OF TYPE
$K3^{[n]}$
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 23 / Issue 5 / September 2024
- Published online by Cambridge University Press:
- 22 December 2023, pp. 2051-2080
- Print publication:
- September 2024
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- Article
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We prove existence and unicity of slope-stable vector bundles on a general polarized hyperkähler (HK) variety of type
$K3^{[n]}$ with certain discrete invariants, provided the rank and the first two Chern classes of the vector bundle satisfy certain equalities. The latter hypotheses at first glance appear to be quite restrictive, but, in fact, we might have listed almost all slope-stable rigid projectively hyperholomorphic vector bundles on polarized HK varieties of type 
$K3^{[n]}$ with 
$20$ moduli.
