Logarithmic Stable Maps

Abstract

We introduce the notion of a logarithmic stable map from a minimal log prestable curve to a log twisted semi-stable variety of form $xy=0$. We study the compactification of the moduli spaces of such maps and provide a perfect obstruction theory, applicable to the moduli spaces of (un)ramified stable maps and stable relative maps. As an application, we obtain a modular desingularization of the main component of Kontsevich's moduli space of elliptic stable maps to a projective space.

30 pages, Corrected Typos, To appear in the proceedings volume of the conference "New developments in Algebraic Geometry, Integrable Systems and Mirror symmetry", RIMS, Kyoto, Jan. 7-11, 2008

References in corpus (2)

• A Generalization of Fulton-MacPherson Configuration Spaces
• Twisted stable maps to tame Artin stacks

Cited by in corpus (11)

• Orbifold techniques in degeneration formulas
• Logarithmic Geometry and Moduli
• Stable logarithmic maps to Deligne--Faltings pairs II
• The Evaluation Space of Logarithmic Stable Maps
• Logarithmic Gromov-Witten invariants
• The degeneration formula for logarithmic expanded degenerations
• Expanded degenerations and pairs
• Strong approximation over function fields
• Comparison of two desingularization of the Kontsevich's moduli space of elliptic stable maps
• Log geometry and exploded manifolds
• Alternate compactifications of the moduli space of genus one maps