Lagrangian subbundles of orthogonal bundles of odd rank over an algebraic curve

2014/02/12 by Insong Choe, Choe, Insong, George H. Hitching +1
Mathematics · #14H60 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1402.2816

openalex publication_date 2014/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An orthogonal bundle over a curve has an isotropic Segre invariant determined by the maximal degree of a Lagrangian subbundle. This invariant, and the induced stratifications on moduli spaces of orthogonal bundles, were studied for bundles of even rank in [4]. In this paper, we obtain analogous results for bundles of odd rank. We obtain a sharp upper bound on the isotropic Segre invariant. We show the irreducibility of the induced strata on the moduli spaces of orthogonal bundles of odd rank, and compute their dimensions. As a key ingredient of the proofs, we study the correspondence between Lagrangian subbundles of orthogonal bundles of even and odd rank.

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