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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

6 votes
3 answers
2k views

Flatness over non-reduced schemes

Is any family of hypersurfaces of fixed degree d (in a projective space of dimension n) over a non-reduced base flat? This is true over reduced bases (assume everything Noetherian), since the Hilbert …
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