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arXiv · 2502.05294

Hecke transformation for orthogonal bundles over curves

Christian Pauly·Hacen Zelaci
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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 $L \subset E_{2x}$ at some point $x \in X$. 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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Christian Pauly, Hacen Zelaci. 2025-02-07. Hecke transformation for orthogonal bundles over curves. https://arxiv.org/abs/2502.05294

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