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.
Palabras Clave: Atiyah bundle; Split Lie algebroid; Nonsplit Lie algebroid; Connection
Índice de impacto JCR-JIF y cuartil WoS: 0,800 - Q2 (2025)
Referencia DOI:
https://doi.org/10.1016/j.jalgebra.2025.05.020
Publicado en papel: Noviembre 2025.
Publicado on-line: Junio 2025.
Cita:
D. Alfaya, I. Biswas, P. Kumar, A. Singh, "A criterion for holomorphic Lie algebroid connections", Journal of Algebra, Vol. 681, pp. 343 - 366, Noviembre 2025. [Online: Junio 2025] doi: 10.1016/j.jalgebra.2025.05.020
