Logarithmic Stable Maps

Details Logarithmic Stable Maps Logarithmic Stable Maps

2008-07-23

arxiv.org/abs/0807.3611v2

Mathematics

Algebraic Geometry

30 pages, Corrected Typos, To appear in the proceedings volume of the conference "New developments in Algebraic Geometry, Inte

Scientific paper

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.

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