Virtual normalization and virtual fundamental classes

Details Virtual normalization and virtual fundamental classes Virtual normalization and virtual fundamental classes

2011-02-21

arxiv.org/abs/1102.4294v1

Mathematics

Algebraic Geometry

to appear in Proceedings of the American Mathematical Society

Scientific paper

In this paper, we compare the virtual fundamental classes of the stacks of $(g,\beta,\mu)$-stable ramified maps $\bar{\mathfrak U}_{g,\mu}(X,\beta)$ and of $(g,\beta,\mu)$-log stable ramified maps $\bar{\mathfrak U}^{\mathrm{log}}_{g,\mu}(X,\beta)$. For that we will see how they are identified via virtual normalization and then apply Costello's push-forward formula.

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