2024/05/31 by Sujoy Chakraborty, Chakraborty, Sujoy, Arjun Paul +1
Mathematics · #14A21 #14D23 #14H60 #53B15 #53C05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2405.20699
openalex publication_date 2024/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a smooth complex projective variety equipped with an action of a linear algebraic group G over ℂ. Let D be a reduced effective divisor on X that is invariant under the G--action on X. Let sD be the canonical section of OX(D) vanishing along D. Given a positive integer r, consider the stack \mathfrakX := \mathfrakX(OX(D), sD, r) of r-th roots of (OX, sD) together with the natural morphism π: \mathfrakX → X. Under the assumption that G has no non-trivial characters, we show that the G--action on X naturally lifts to a G--action on \mathfrakX such that π become G--equivariant, and the tautological invertible sheaf \mathscrM on \mathfrakX admits a linearization of this G--action. Finally, we define the notions of G--equivariant logarithmic connections on \mathfrakX and G--equivariant parabolic connections on X with rational parabolic weights along D, and establish an equivalence between the category of G--equivariant logarithmic connections on \mathfrakX and the category of G--equivariant parabolic connections on X with rational parabolic weights along D.