2014/05/12 by Brian Osserman, Osserman, Brian
Mathematics · #14D06 #14H51 #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.1405.2937
openalex publication_date 2014/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
In order to prove new existence results in Brill-Noether theory for rank-2 vector bundles with fixed special determinant, we develop foundational definitions and results for limit linear series of higher-rank vector bundles. These include two entirely new constructions of "linked linear series" generalizing earlier work of the author for the classical rank-1 case, as well as a new canonical stack structure for the previously developed theory due to Eisenbud, Harris and Teixidor i Bigas. This last structure is new even in the classical rank-1 case, and yields the first proper moduli space of Eisenbud-Harris limit linear series for families of curves. We also develop results comparing these three constructions.