Higher order Jacobians, Hessians and Milnor algebras

We introduce and study higher order Jacobian ideals, higher order and mixed Hessians, higher order polar maps, and higher order Milnor algebras associated to a reduced projective hypersurface. We relate these higher order objects to some standard graded Artinian Gorenstein algebras, and we study the...

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Bibliographic Details
Published inCollectanea mathematica (Barcelona) Vol. 71; no. 3; pp. 407 - 425
Main Authors Dimca, Alexandru, Gondim, Rodrigo, Ilardi, Giovanna
Format Journal Article
LanguageEnglish
Published Milan Springer Milan 01.09.2020
Springer Nature B.V
Subjects
Algebra
Analysis
Applications of Mathematics
Geometry
Hyperspaces
Jacobians
Mathematics
Mathematics and Statistics
05E40
Jacobian ideal
Standard graded Artinian Gorenstein algebras
Secondary 13D40
Hilbert functions
Lefschetz properties
Primary 13A02
13E10
Hessian
Polar mapping
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Summary:We introduce and study higher order Jacobian ideals, higher order and mixed Hessians, higher order polar maps, and higher order Milnor algebras associated to a reduced projective hypersurface. We relate these higher order objects to some standard graded Artinian Gorenstein algebras, and we study the corresponding Hilbert functions and Lefschetz properties.
ISSN:0010-0757
2038-4815
DOI:10.1007/s13348-019-00266-1