1. A remark on the moduli space of Lie algebroid λ-connections.
- Author
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Keshari, Parul and Singh, Anoop
- Subjects
- *
RIEMANN surfaces , *AUTOMORPHISM groups , *VECTOR bundles , *PICARD groups , *VECTOR spaces - Abstract
Let X be a compact Riemann surface of genus g ≥ 3 . Let L = (L , [. ,. ] , ♯) be a holomorphic Lie algebroid over X of rank one and degree (L) < 2 − 2 g . We consider the moduli space of holomorphic L λ -connections over X, where λ ∈ C . We compute the Picard group of the moduli space of L λ -connections by constructing an explicit smooth compactification of the moduli space of those L λ -connections whose underlying vector bundle is stable such that the complement is a smooth divisor. We also show that the automorphism group of the moduli space of L λ -connections fits into a short exact sequence that involves the automorphism group of the moduli space of stable vector bundle over X. For λ = 1, we get Lie algebroid de Rham moduli space of L -connections and we determine its Chow group. Communicated by Manuel Reyes [ABSTRACT FROM AUTHOR]
- Published
- 2024
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