2011/08/24 by Brian Osserman, Osserman, Brian
Mathematics · Physics and Astronomy · #14H60 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #FOS: Mathematics #Nonlinear Waves and Solitons #math.AG #msc:14H60
paper · pdf · doi:10.48550/arxiv.1108.4968
17 pages
arxiv created 2011/08/24 · openalex publication_date 2011/08/24 · arxiv updated 2011/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Continuing our previous study of modified expected dimensions for rank-2 Brill-Noether loci with prescribed special determinants, we introduce a general framework which applies a priori for arbitrary rank, and use it to prove modified expected dimension bounds in several new cases, applying both to rank 2 and to higher rank. The main tool is the introduction of generalized alternating Grassmannians, which are the loci inside Grassmannians corresponding to subspaces which are simultaneously isotropic for a family of multilinear alternating forms on the ambient vector space. In the case of rank 2 with 2-dimensional spaces of sections, we adapt arguments due to Teixidor i Bigas to show that our new modified expected dimensions are in fact sharp.