Non-defectivity of Grassmannian bundles over a curve

2015/01/06 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.1501.01280

openalex publication_date 2015/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Gr(2, E) be the Grassmann bundle of two-planes associated to a general bundle E over a curve X. We prove that an embedding of Gr(2, E) by a certain twist of the relative Plücker map is not secant defective. This yields a new and more geometric proof of the Hirschowitz-type bound on the Lagrangian Segre invariant for orthogonal bundles over X, analogous to those given for vector bundles and symplectic bundles in [2, 3]. From the non-defectivity we also deduce an interesting feature of a general orthogonal bundle over X, contrasting with the classical and symplectic cases: Any maximal Lagrangian subbundle intersects at least one other maximal Lagrangian subbundle in positive rank.

Related

• Lagrangian subbundles of symplectic bundles over a curve
• Non-Defectivity of Grassmannians of planes
• Lagrangian subbundles of orthogonal bundles of odd rank over an algebraic curve
• Secant varieties and Hirschowitz bound on vector bundles over a curve
• Orthogonal bundles over curves in characteristic two