Unexpected curves and Togliatti‐type surfaces

Justyna Szpond

Mathematische Nachrichten, 2020, vol. 293, issue 1, 158-168

Abstract: 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 XB of degree 7 in P5 with its osculating spaces of order 2 which in every point of XB have dimension lower than expected. We put this result in perspective with earlier examples of surfaces with defective osculating spaces due to Shifrin and Togliatti. Our considerations are rendered by an analysis of Lefschetz Properties of ideals associated with the studied surfaces.

Date: 2020
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