## Advanced Studies in Pure Mathematics

### Logarithmic stable maps

Bumsig Kim

#### 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.

#### Article information

Dates
First available in Project Euclid: 24 November 2018

https://projecteuclid.org/ euclid.aspm/1543085924

Digital Object Identifier
doi:10.2969/aspm/05910167

Mathematical Reviews number (MathSciNet)
MR2683209

Zentralblatt MATH identifier
1216.14023

#### Citation

Kim, Bumsig. Logarithmic stable maps. New Developments in Algebraic Geometry, Integrable Systems and Mirror Symmetry (RIMS, Kyoto, 2008), 167--200, Mathematical Society of Japan, Tokyo, Japan, 2010. doi:10.2969/aspm/05910167. https://projecteuclid.org/euclid.aspm/1543085924