Universal limit linear series and descent of moduli spaces

2017/08/31 by Max Lieblich, Brian Osserman
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #Algebraic geometry #Descent (aeronautics) #Limit (mathematics) #Mathematical Dynamics and Fractals #Moduli #Moduli of algebraic curves #Moduli space #Stack (abstract data type) #math.AG #msc:14D06 #msc:14H51 #msc:14P99

paper · pdf · doi:10.1007/s00229-018-1049-5

published as manuscripta math. (2019) 159: 13 · 23 pages, journal reference added

openalex created_date 2017/08/08 · openalex publication_date 2018/07/03 · arxiv created 2019/10/28 · arxiv updated 2019/10/30 · openalex updated_date 2026/08/05

Abstract

We introduce a formalism of descent of moduli spaces, and use it to produce limit linear series moduli spaces for families of curves in which the components of fibers may have monodromy. We then construct a universal stack of limit linear series over the stack of semistable curves of compact type, and produce new results on existence of real curves with few real linear series.

Citations

• The irreducibility of the space of curves of given genus
• Algebraic Geometry
• Éléments de géométrie algébrique : IV. Étude locale des schémas et des morphismes de schémas, Troisième partie
• Éléments de géométrie algébrique : IV. Étude locale des schémas et des morphismes de schémas, Quatrième partie