2018/10/15 by Justyna Szpond, Szpond, Justyna
Mathematics · #13A15 #13E10 #13F20 #14C20 #14J26 #14N05 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:13A15 #msc:13E10 #msc:13F20 #msc:14C20 #msc:14J26 #msc:14N05
paper · pdf · doi:10.48550/arxiv.1810.06607
13 pages, v.3 the new version reflects comments from prof. Ragni Piene on Shiffrin conjecture
arxiv created 2019/05/14 · arxiv updated 2019/05/15
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 X of degree 7 in P5 with its osculating spaces of order 2 which in every point of X 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.