Comparison of two desingularizations of the moduli space of elliptic stable maps
J. Korean Math. Soc.
Published online November 27, 2020
Hyenho Lho
Chungnam National University
Abstract : We study the geometry of the moduli space of elliptic stable maps to projective space. The main component of the moduli space of elliptic stable maps is singular. There are two different way to desingularize this space. One is Vakil-Zinger’s desingularization and the other is via the moduli space of logarithmic stable maps. Our main result is a proof of the direct geometric relation- ship between these two spaces. For degree less than or equal to 3, we prove that the moduli space of logarithmic stable maps can be obtained by blowing up Vakil-Zinger’s desingularization.
Keywords : moduli space of stable maps
MSC numbers : 14N35
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