Moduli spaces $M_{g,n}(W)$ for surfaces

Abstract

We construct and prove the projectiveness of the moduli spaces which are natural generalizations to the case of surfaces of the following: 1) $M_{g,n}$, the moduli space of $n$-marked stable curves, 2) $M_{g,n}(W)$, the moduli space of $n$-marked stable maps to a variety $W$.

21 pages, written in AMS-LaTeX

References in corpus (1)

• Semistable Minimal Models of Threefolds in Positive or Mixed Characteristic

Cited by in corpus (12)

• Compact moduli of plane curves
• Nonexistence of asymptotic GIT compactification
• Wall crossing for K-moduli spaces of plane curves
• Pluricanonical maps of stable log surfaces
• Heterotic-Type IIA Duality and Degenerations of K3 Surfaces
• Looking for rational curves on cubic hypersurfaces
• Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties
• The Geometry and Moduli of K3 Surfaces
• Moduli of surfaces in ${\mathbb{P}}^3$
• Geometric invariant theory and moduli spaces of maps
• Semistable divisorial contractions
• The Calabi conjecture and K-stability