Picard Groups of Stacky Curves

2023/06/14 by Rose Lopez, Lopez, Rose · 3 citations
Mathematics · Engineering · #Geometric and Algebraic Topology #Algebraic Geometry and Number Theory #Advanced Numerical Analysis Techniques

paper · pdf · doi:10.48550/arxiv.2306.08227

Abstract

We describe the Picard group of a tame stacky curve as an extension of two groups, which depend on the gerbe class of the curve over its rigidification, a stacky curve with trivial generic stabilizer, and the residual gerbes of the rigidification. After presenting the general formulation, we compute some specific examples. In particular, we provide an example highlighting the fact that the extension of the groups truly depends on the class of the gerbe.

Cited by

• Tame nodal stacky curves
• The Integral Chow Rings of the Moduli Stacks of Hyperelliptic Prym Pairs III
• Brauer groups of tame stacky curves and their μ_r-gerbes

Related

• Brauer groups of tame stacky curves and their μ_r-gerbes
• On the Picard group scheme of the moduli stack of stable pointed curves
• The Picard groups of the stacks Y₀(2) and Y₀(3)
• The Picard Group of the Stack of Pointed Smooth Cyclic Covers of the Projective Line
• The Picard group of the universal moduli space of vector bundles on\n stable curves