Mathematics – Algebraic Geometry
Scientific paper
2011-10-24
Mathematics
Algebraic Geometry
21 pages, 4 figures
Scientific paper
We prove that r independent homogeneous polynomials of the same degree d become dependent when restricted to any hyperplane if and only if their inverse system parameterizes a variety whose (d-1)-osculating spaces have dimension smaller than expected. This gives an equivalence between an algebraic notion (called Weak Lefschetz Property) and a differential geometric notion, concerning varieties which satisfy certain Laplace equations. In the toric case, some relevant examples are classified and as byproduct we provide counterexamples to Ilardi's conjecture.
Mezzetti Emilia
Miro'-Roig Rosa M.
Ottaviani Giorgio
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