A criterion for holomorphic Lie algebroid connections
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2025-11-01Estado
info:eu-repo/semantics/publishedVersionMetadatos
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Resumen
Given a holomorphic Lie algebroid (V,ø) on a compact connected Riemann surface X, we give a necessary and sufficient condition for a holomorphic vector bundle E on X to admit a holomorphic Lie algebroid connection. If (V,ø) is nonsplit, then every holomorphic vector bundle on X admits a holomorphic Lie algebroid connection for (V,ø). If (V,ø) is split, then a holomorphic vector bundle E on X admits a holomorphic Lie algebroid connection if and only if the degree of each indecomposable component of E is zero. Given a holomorphic Lie algebroid (V,ø) on a compact connected Riemann surface X, we give a necessary and sufficient condition for a holomorphic vector bundle E on X to admit a holomorphic Lie algebroid connection. If (V,ø) is nonsplit, then every holomorphic vector bundle on X admits a holomorphic Lie algebroid connection for (V,ø). If (V,ø) is split, then a holomorphic vector bundle E on X admits a holomorphic Lie algebroid connection if and only if the degree of each indecomposable component of E is zero.