Timeline for What is the degree zero Gromov-Witten invariant of quintic threefold?

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Jan 31, 2018 at 7:04	comment	added	keaton		Thank you for Jason and Honglu and I'm sorry for my late reply. I also found a good reference for degree zero Gromov-Witten invariant written by R. Pandharipande : arxiv.org/abs/math/0302077
Jan 9, 2018 at 22:02	comment	added	Honglu		In addition to Jason's comments, when $g\geq 2$, $\overline M_{g,0}(X,0)=\overline M_{g}\times X$. The obstruction bundle is given by $\mathbb E^\vee \boxtimes TX$ where $\mathbb E$ is the hodge bundle. Then I believe a splitting principle computation plus a little intersection theory on $\overline M_g$ should give you the result. When $g=1$ you need one marking, and the computation follows from the similar idea.
Jan 9, 2018 at 20:43	comment	added	Jason Starr		Typo correction: "... stable maps to $X$ is an empty stack." --> " ... stable maps to $X$ with zero homology class is an empty stack."
Jan 9, 2018 at 18:13	comment	added	Jason Starr		For every complex manifold $X$, the moduli stack of genus-$0$, $0$-pointed stable maps to $X$ is an empty stack. Thus, it is (tautologically) transverse, the virtual fundamental class equals the actual fundamental class, this is the zero class, and every pairing of this fundamental class against cohomology classes is zero.
Jan 9, 2018 at 15:06	history	edited	Martin Sleziak	CC BY-SA 3.0	capitalization
Jan 9, 2018 at 14:45	history	asked	keaton	CC BY-SA 3.0