Answer by Roberto Pignatelli for Is each rationally chain connected surface...
By the comments of abx you only need an answer to question $3$. You get easily an answer if you assume the results in the classical book of Beauville on algebraic surfaces.Namely, if $S$ is uniruled,...
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Consider a 2-dimensional smooth projective algebraic surface S over complex numbers. Could you recommend any exact references to the proofs of the following assertions (of course, if they are true):If...
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