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Francesco Polizzi
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Let $S$ be a projective K3 surface. Then is there always a smooth projective 3-fold $V$ that has $S$ as its anticanonical section?

Let $S$ be a projective K3 surface. Then is there always a smooth projective 3-fold that has $S$ as its anticanonical section?

Let $S$ be a projective K3 surface. Then is there always a smooth projective 3-fold $V$ that has $S$ as its anticanonical section?

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Creg
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K3 surface as an anticanonical section

Let $S$ be a projective K3 surface. Then is there always a smooth projective 3-fold that has $S$ as its anticanonical section?