Linked symplectic forms and limit linear series in rank 2 with special determinant

2014/05/13 by Brian Osserman, Osserman, Brian, Montserrat Teixidor i Bigas +2
Mathematics · #14D06 #14H51 #14H60 #14M15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #math.AG #msc:14D06 #msc:14H51 #msc:14H60 #msc:14M15

paper · pdf · doi:10.48550/arxiv.1405.3314

46 pages, 1 figure

arxiv created 2014/05/13 · openalex publication_date 2014/05/13 · arxiv updated 2014/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize the prior linked symplectic Grassmannian construction, applying it to to prove smoothing results for rank-2 limit linear series with fixed special determinant on chains of curves. We apply this general machinery to prove new results on nonemptiness and dimension of rank-2 Brill-Noether loci in a range of degrees.

Citations

• Stable curves and special divisors: Petri's conjecture

Related

• Linked Grassmannians and crude limit linear series
• Limit linear series moduli stacks in higher rank
• Brill-Noether loci with fixed determinant in rank 2
• Linked alternating forms and linked symplectic Grassmannians
• Special determinants in higher-rank Brill-Noether theory