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Unexpected curves and Togliatti‐type surfaces

2019; Wiley; Volume: 293; Issue: 1 Linguagem: Inglês

10.1002/mana.201800455

1522-2616

Justyna Szpond,

Polynomial and algebraic computation

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 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 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.