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I have a couple of question about the proof of Lemma 1.20.5 from Janos Kolloar's Lecture on Resolution of Singularities (page 19): Lemma 1.20.5 Let $C$ be a reduced, irreducible projective curve (=1D ...

Let $S$ be a smooth quasi-projective curve over the complex numbers. Let $P$ be a closed point in $S$. Let $f:\mathcal X \to S$ be a polarized family of smooth projective connected varieties. To this ...

This question is about properties of Isom-schemes that are well-known over algebraically closed fields. Let $K$ be a field of characteristic zero, let $C$ be a smooth projective geometrically ...