Timeline for Cohomology groups of the complement of an ample singular divisor

6 events

when toggle format	what		by	license	comment
May 10, 2018 at 13:13	answer	added	Nikolay Konovalov		timeline score: 1
May 4, 2018 at 20:17	history	edited	Nikolay Konovalov	CC BY-SA 4.0	edited body
May 2, 2018 at 15:38	answer	added	Jason Starr		timeline score: 1
May 2, 2018 at 11:10	comment	added	Nikolay Konovalov		@JasonStarr Thanks, but I assume that $Y$ is irreducible. Maybe I should say it more clear.
May 2, 2018 at 10:29	comment	added	Jason Starr		If $X$ equals $\mathbb{CP}^1 \times \mathbb{CP}^1$, and if $Y$ equals $(\mathbb{CP}^1\times\{\infty\}) \cup (\{\infty \} \times \mathbb{CP}^1)$, then $U$ equals $\mathbb{C}\times \mathbb{C}$, which has vanishing $H^2$ since it is contractible. On the other hand, the Poincar'e dual of the homology class $[\mathbb{CP}^1\times \{ \infty \}] - [\{ \infty \} \times \mathbb{CP}^1]$ is a nonzero, primitive class in $H^2(X;\mathbb{Q})$.
May 2, 2018 at 5:59	history	asked	Nikolay Konovalov	CC BY-SA 4.0