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VOL. 59 | 2010 Logarithmic stable maps
Bumsig Kim

Editor(s) Masa-Hiko Saito, Shinobu Hosono, Kōta Yoshioka

## 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.

## Information

Published: 1 January 2010
First available in Project Euclid: 24 November 2018

zbMATH: 1216.14023
MathSciNet: MR2683209

Digital Object Identifier: 10.2969/aspm/05910167

Subjects:
Primary: 14H10
Secondary: 14N35

Rights: Copyright © 2010 Mathematical Society of Japan

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Vol. 59 • 1 January 2010