Generalizing the GAGA Principle

Abstract

This paper generalizes the fundamental GAGA results of Serre cite{MR0082175} in three ways---to the non-separated setting, to stacks, and to families. As an application of these results, we show that analytic compactifications of ${\mathcal{M}}_{g,n}$ possessing modular interpretations are algebraizable.

19 pages

References in corpus (7)

• Tannaka Duality for Geometric Stacks
• Finite Hilbert stability of (bi)canonical curves
• Weakly proper moduli stacks of curves
• The Hilbert Stack
• Singularities with G_m-action and the log minimal model program for ${\bar{M}}_g$
• Log minimal model program for the moduli space of stable curves: The second flip
• Existence of good moduli spaces for A_k-stable curves

Cited by in corpus (2)

• A predicted distribution for Galois groups of maximal unramified extensions
• General GLSM Invariants and Their Cohomological Field Theories