Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



A compactification of the space of maps from curves

Authors: Bumsig Kim, Andrew Kresch and Yong-Geun Oh
Journal: Trans. Amer. Math. Soc. 366 (2014), 51-74
MSC (2010): Primary 14N35; Secondary 14D20
Published electronically: April 25, 2013
MathSciNet review: 3118390
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Abstract: We construct a new compactification of the moduli space of maps from pointed nonsingular projective stable curves to a nonsingular projective variety with prescribed ramification indices at the points. It is shown to be a proper Deligne-Mumford stack equipped with a natural virtual fundamental class.

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Bumsig Kim
Affiliation: School of Mathematics, Korea Institute for Advanced Study, 85 Heogiro, Dongdaemun-gu, Seoul, 130-722, Republic of Korea

Andrew Kresch
Affiliation: Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland

Yong-Geun Oh
Affiliation: Department of Mathematics, University of Wisconsin, Madison, 480 Lincoln Drive, Madison, Wisconsin 53706-1388 — and — Department of Mathematics, POSTECH, Pohang, 790-784, Republic of Korea

Received by editor(s): August 21, 2011
Published electronically: April 25, 2013
Additional Notes: The first author was partially supported by the NRF grant 2011-0001181 through ASARC
The second author was partially supported by a grant from the SNF
The third author was partially supported by the NSF grant DMS 0904197 and acknowledges the financial support and excellent research environment of KIAS over many years of summer visits
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.