2023/10/03 by Kuntal Banerjee, Steven Rayan, Banerjee, Kuntal +1
Mathematics · #14D20 #14H60 #20B35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2310.02413
openalex publication_date 2023/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We explore a strong categorical correspondence between isomorphism classes of sheaves of arbitrary rank on a given algebraic curve and twisted pairs on another algebraic curve, mostly from a linear-algebraic standpoint. In a particular application, we realize a generic elliptic curve as a spectral cover of the complex projective line ℙ1 and then construct examples of cyclic pairs and co-Higgs bundles over ℙ1. By appealing to a composite push-pull projection formula, we conjecture an iterated version of spectral correspondence. We prove this conjecture for a particular class of spectral covers of \mathbb P1 through Galois-theoretic arguments. The proof relies upon a classification of Galois groups into primitive and imprimitive types. In this context, we revisit a classical theorem of Ritt.