Logarithmic Stable Maps
arXiv:0807.3611
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 . 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