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The purpose of this note is to establish a direct link between the theory of unexpected hypersurfaces and varieties with defective osculating behavior. We identify unexpected plane curves of degree 4 as sections of a rational surface of degree 7 in with its osculating spaces of order 2 which in every point of have dimension lower than expected. We put this result in perspective with earlier...
The purpose of this note is to study initial sequences of 0–dimensional subschemes of Hirzebruch surfaces and classify subschemes whose initial sequence has the minimal possible growth.
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