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Rationally connectedness and O'Grady's generalized Franchetta conjecture for K3 surfaces
O'Grady's generalized Franchetta conjecture asks whether any codimension two cycle on the universal polarized K3 surfaces restricts to a multiple of the Beauville--Voisin class on a given K3 surface. We apply Bergeron--Li's result on the cohomology of universal K3 surfaces to give an affirmative ans
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