We prove existence and unicity of slope-stable vector bundles on a general polarized hyperkahler (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.
RIGID STABLE VECTOR BUNDLES ON HYPERKÄHLER VARIETIES OF TYPE $K3^{[n]}$ / O'Grady, Kieran G.. - In: JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU. - ISSN 1474-7480. - 23:5(2024), pp. 2051-2080. [10.1017/s1474748023000452]
RIGID STABLE VECTOR BUNDLES ON HYPERKÄHLER VARIETIES OF TYPE $K3^{[n]}$
O'Grady, Kieran G.
2024
Abstract
We prove existence and unicity of slope-stable vector bundles on a general polarized hyperkahler (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.| File | Dimensione | Formato | |
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