Hecke transformation for orthogonal bundles over curves

2025/02/07 by Pauly, Christian, Zelaci, Hacen
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.05294

Abstract

Given an orthogonal bundle E over a smooth projective curve X we define a Hecke transformation in the moduli space of orthogonal bundles by performing an elementary transformation with respect to a Lagrangian submodule L ⊂ E_2x at some point x ∈ X. We show that the analogue of Tyurin's duality theorem holds for orthogonal bundles. Special cases of orthogonal bundles of ranks 2,3,4 and 6 are studied in detail.

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