Comparison of two desingularization of the Kontsevich's moduli space of elliptic stable maps

Details Comparison of two desingularization of the Kontsevich's moduli space of elliptic stable maps Comparison of two desingularization of the Kontsevich's moduli space of elliptic stable maps

2011-08-23

arxiv.org/abs/1108.4617v2

Mathematics

Algebraic Geometry

Scientific paper

It is known that the main component of the Kontsevich's moduli space of elliptic stable maps is singular. There are two different desingularizations. One is Vakil-Zinger's desingularization and the other is the moduli space of logarithmic stable maps. When the degree is less then or equal to 3 and the target is $\mathbb{P}^{n}$, we show that the moduli space of logarithmic stable maps can be obtained by blowing up Vakil-Zinger's desingularization.

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