Universal limit linear series and descent of moduli spaces

TL;DR

This paper develops a formalism for descending moduli spaces to construct universal limit linear series spaces over families of curves, including those with monodromy, and explores real curve applications.

Contribution

It introduces a descent formalism for moduli spaces and constructs a universal stack of limit linear series over semistable curves of compact type.

Findings

Constructed limit linear series moduli spaces for families with monodromy

Developed a universal stack over the stack of semistable curves

Proved existence results for real curves with few real linear series

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.