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Dec 17, 2011 at 10:39 history undeleted S. Carnahan
Aug 19, 2011 at 3:11 history deleted Thom
Aug 18, 2011 at 2:02 comment added Maharana By a result of Nori (Corr 2.4B in "Zariski's conjecture and related problems"), if $C^2>0$ for an irreducible curve $C$ on a surface $X$ then $\pi_1(C)$ surjects on $\pi_1(X)$. Since $K^2>0$ for a general type surface it follows that $\Sigma_k^2>0$ as well, in your question, hence the required surjection.
Aug 17, 2011 at 19:44 answer added J.C. Ottem timeline score: 2
Aug 17, 2011 at 18:41 history asked Thom CC BY-SA 3.0