Comparison of two desingularizations of the moduli space of elliptic stable maps

Hyenho Lho

doi:10.4134/JKMS.j200163

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2021; 58(2): 501-523

Online first article November 27, 2020 Printed March 1, 2021

https://doi.org/10.4134/JKMS.j200163

Comparison of two desingularizations of the moduli space of elliptic stable maps

Hyenho Lho

Chungnam National University

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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 ways 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 relationship 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: Desingularization, Logarithmic stable map

MSC numbers: 14D23