Hermitian–Yang–Mills Connections on Collapsing Elliptically Fibered K3 Surfaces

Let [Formula: see text] be an elliptically fibered K3 surface, admitting a sequence [Formula: see text] of Ricci-flat metrics collapsing the fibers. Let V be a holomorphic SU(n) bundle over X, stable with respect to [Formula: see text] . Given the corresponding sequence [Formula: see text] of Hermit...

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Detalles Bibliográficos
Autores principales: Datar, Ved, Jacob, Adam
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8741718/
https://www.ncbi.nlm.nih.gov/pubmed/35110958
http://dx.doi.org/10.1007/s12220-021-00808-9
Descripción
Sumario:Let [Formula: see text] be an elliptically fibered K3 surface, admitting a sequence [Formula: see text] of Ricci-flat metrics collapsing the fibers. Let V be a holomorphic SU(n) bundle over X, stable with respect to [Formula: see text] . Given the corresponding sequence [Formula: see text] of Hermitian–Yang–Mills connections on V, we prove that, if E is a generic fiber, the restricted sequence [Formula: see text] converges to a flat connection [Formula: see text] . Furthermore, if the restriction [Formula: see text] is of the form [Formula: see text] for n distinct points [Formula: see text] , then these points uniquely determine [Formula: see text] .

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