Timeline for Basic property of Gromov-witten invariant

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Aug 7, 2017 at 11:42	comment	added	Jason Starr		The proper pushforward map in homology, resp. Chow groups, is a graded homomorphism that preserves the homological degree, i.e., $H_q(\overline{M}_{0,n}\times \mathbb{P}^r)\to H_q(\mathbb{P}^r)$, resp. $\text{CH}_p(\overline{M}_{0,n}\times \mathbb{P}^r)\to \text{CH}_p(\mathbb{P}^r)$. The fundamental class of $\overline{M}_{0,n}\times \mathbb{P}^r$ is in degree $2(r+(n-3))$, resp. in $\text{CH}_{r+(n-3)}(\overline{M}_{0,n}\times \mathbb{P}^r)$. Since the homology groups, resp. Chow groups, of $\mathbb{P}^r$ vanish in degrees $>2r$, resp. $>r$, the pushforward is nonzero if and only if $n=3$.
S Aug 7, 2017 at 11:36	history	suggested	Mee Seong Im	CC BY-SA 3.0	improved formatting
Aug 7, 2017 at 11:23	review	Suggested edits
S Aug 7, 2017 at 11:36
Aug 7, 2017 at 11:23	comment	added	YCor		It would help if you include more context instead of embedding a scanned excerpt from a book.
Aug 7, 2017 at 11:22	history	edited	YCor		edited tags
Aug 7, 2017 at 11:04	history	asked	mamiemamie	CC BY-SA 3.0