A remark on the moduli space of Lie algebroid λ-connections

Abstract

Let X be a compact Riemann surface of genus (Formula presented.). Let (Formula presented.) be a holomorphic Lie algebroid over X of rank one and degree (Formula presented.). We consider the moduli space of holomorphic (Formula presented.) -connections over X, where (Formula presented.). We compute the Picard group of the moduli space of (Formula presented.) -connections by constructing an explicit smooth compactification of the moduli space of those (Formula presented.) -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 (Formula presented.) -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 (Formula presented.) -connections and we determine its Chow group. Communicated by Manuel Reyes. © 2024 Taylor & Francis Group, LLC.