Laplace Equations and the Weak Lefschetz Property
By Emilia Mezzettiaaa, Rosa M. Miré-Roig, Giorgio Ottaviani. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2011
87 citations recorded by the source corpus.
Abstract 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 the Weak Lefschetz Property) and a differential geometric notion, concerning varieties that satisfy certain Laplace equations. In the toric case, some relevant examples are classified, and as a byproduct we provide counterexamples to Ilardi's conjecture.
Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/02e98383c1264dac6e4807be314890ab37594d20
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In Computational Theory and Mathematics
In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- On higher Hessians and the Lefschetz properties (2015, background): “ert vector. Stanley in [St2] constructed the first example of a nonunimodal Artinian Gorenstein algebra. After that, others authors studied nonunimodality and its implications ([BI, Bo, Bol, MNZ]). In [MRO] the authors introduced a geometric approach which allowed them to produce other examples of Ar”