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Virtual normalization and virtual fundamental classes

Author: Alberto López Martín
Journal: Proc. Amer. Math. Soc. 140 (2012), 2235-2240
MSC (2010): Primary 14A20; Secondary 14D23
Published electronically: November 4, 2011
MathSciNet review: 2898687
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Abstract: In this paper, we compare the virtual fundamental classes of the stacks of $ (g,\beta ,\mu )$-stable ramified maps $ \overline {\mathfrak{U}}_{g,\mu }(X,\beta )$ and of $ (g,\beta ,\mu )$-log stable ramified maps $ \overline {\mathfrak{U}}^{\mathrm {log}}_{g,\mu }(X,\beta )$. For that we will see how they are identified via virtual normalization and then apply Costello's push-forward formula.

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Additional Information

Alberto López Martín
Affiliation: Institut für Mathematik, Universität Zürich-Irchel, Zürich, CH-8057, Switzerland
Address at time of publication: Department of Mathematics, Bromfield-Pearson Hall, Tufts University, 503 Boston Avenue, Medford, Massachusetts 02155

Received by editor(s): September 15, 2010
Received by editor(s) in revised form: December 22, 2010, and February 18, 2011
Published electronically: November 4, 2011
Additional Notes: The author was supported in part by the Swiss National Science Foundation project 200020_126756.
Communicated by: Lev Borisov
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.