Compactifying the space of stable maps

Abstract

We define two equivalent notions of twisted stable map from a curve to a Deligne-Mumford stack with projective moduli space, and we prove that twisted stable maps of fixed degree form a complete Deligne-Mumford stack with projective moduli space.

34 pages; Latex 2e. The following devices were used to reduce the authors' publication count: 1. new section on canonical contractions and functoriality added, and 2. introduction expanded based on our research announcement math.AG/9811059

References in corpus (2)

• Stable maps and Hurwitz schemes in mixed characteristic
• Complete moduli for families over semistable curves

Cited by in corpus (9)

• Orbifold Quantum Cohomology
• Geometry of meromorphic functions and intersections on moduli spaces of curves
• Topological recursive relations in $H^{2g}(M_{g,n})$
• Complete moduli for families over semistable curves
• Explicit stable models of elliptic surfaces with sections
• The logarithmic gauged linear sigma model
• Twisted bundles and admissible covers
• A Theory of Stacky Fans
• Moduli of twisted spin curves