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Frobenius dilation of Hilbert function, Demailly's conjecture, and varieties of powers
We prove a Frobenius-dilation inequality for Hilbert functions of ideals generated by powers of fixed homogeneous forms in characteristic zero. Via Emsalem--Iarrobino inverse system duality, it yields quantitative fat-point postulation estimates and a new proof of the recent theorem of Ha--Sivakumar
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