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May 23, 2022 at 20:22 comment added Jason Starr Yes, of course the key property in my example above is non-compactness of the Douady space of the sections. Once we have compactness of these, we also have compactness of the Douady spaces of "minimal free rational curves." Then the psi class is ample on the moduli space of such curves, etc.
May 23, 2022 at 11:54 history answered Misha Verbitsky CC BY-SA 4.0