Tame nodal stacky curves

TL;DR

The paper addresses how stacky node structures influence Picard and Brauer groups on tame nodal curves. It combines the Leray spectral sequence, stabilizer cohomology, and pushout/root-stack techniques to produce explicit formulas. The main contributions are precise Picard group descriptions for twisted and doubly-twisted nodes and a complete account of node contributions to the Brauer group, including a nontrivial $Z/2$ case. The results show that nodal stacky nodes are not root stacks and provide tools for moduli and intersection-theory applications.

Abstract

In this paper we analyze the properties of tame nodal stacky curves, in particular twisted curves and \textit{doubly-twisted} curves. Our main results are a complete classification of the possible structures of a tame stacky node, along with computations of the Picard and Brauer groups of nodal stacky curves.

Theorems & Definitions (65)

• Theorem : Lop23, Theorem 1.1
• Theorem : Theorem \ref{['twisted Picard v1']}
• Corollary : Corollary \ref{['balanced twisted Picard']}
• Theorem : Theorem \ref{['doubly-twisted Picard']}
• Theorem : Propositions \ref{['H2 doubly twisted']} and \ref{['H2 twisted']}
• Theorem 2.1: Tsen's Theorem
• Theorem 2.2
• proof
• Proposition 2.3
• proof