Non-defectivity of Grassmannian bundles over a curve
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 Pl\"ucker 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.
Keywords
Cite
@article{arxiv.1501.01280,
title = {Non-defectivity of Grassmannian bundles over a curve},
author = {Insong Choe and George H. Hitching},
journal= {arXiv preprint arXiv:1501.01280},
year = {2015}
}
Comments
Submitted to proceedings of VBAC 2014; Algebraic Varieties: Bundles, Topology, Physics. 13 pp