# Reference request: virtual fundamental class of moduli of stable maps

Let $f:U\longrightarrow \overline{M}_{0,n}(\mathbb{P}^m,d)$ is the universal family with morphism $\pi:U\longrightarrow\mathbb{P}^m$ and let $X\subset\mathbb{P}^m$ be a hypersurface defined by a global section $x$ of $\mathcal{O}(X)$ then $f_{\ast}\pi^{\ast}\mathcal{O}(X)$ is a vectorbundle on $\overline{M}_{0,n}(\mathbb{P}^m,d)$ with global section $f_{\ast}\pi^{\ast}x$. It seems to be known that the zero locus of the section $f_{\ast}\pi^{\ast}x$ is the virtual fundamental class of $\overline{M}_{0,n}(X,\beta)$ (for a suitable $\beta$ ).

Does anyone know a good reference for this? I had a look at the paper of Behrend and Fantechi about virtual fundamental classes, but I was not able to figure this out from that paper. Thank you in advance.

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I'm sorry, but somhow it does not show the Latex-code correctly on my Browser... I hope that's only a problem of my computer :( – Dennis Ochse Sep 24 '12 at 11:36
it seems that closing \$ are missing... – Carlo Beenakker Sep 24 '12 at 11:44
I fixed it. Sometime you have to enclose math in backticks (`) in order to get everything parsed correctly. – Dan Petersen Sep 24 '12 at 11:45
Oops looks like Dan and I were fixing it at the same time. Feel free to un-edit my edit. – Mark Grant Sep 24 '12 at 11:48
Thank you very much, now it looks much better :) – Dennis Ochse Sep 24 '12 at 11:55