Geodesic
Hessian ideals of a homogeneous polynomial and generalized Tjurina algebras
Documenta mathematica, Tome 20 (2015), pp. 689-705

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Using the minors in Hessian matrices, we introduce new graded algebras associated to a homogeneous polynomial. When the associated projective hypersurface has isolated singularities, these algebras are related to some new local algebras associated to isolated hypersurface singularities, which generalize their Tjurina algebras. One consequence of our results is a new very rapid way to determine the number of weighted homogeneous singularities of such a hypersurface.
DOI : 10.4171/dm/502
Classification : 13D40, 14B05, 14J70, 32S05
Mots-clés : projective hypersurfaces, graded algebra, Hessian matrix, weighted homogeneous singularities 
Alexandru Dimca; Gabriel Sticlaru. Hessian ideals of a homogeneous polynomial and generalized Tjurina algebras. Documenta mathematica, Tome 20 (2015), pp. 689-705. doi: 10.4171/dm/502
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     author = {Alexandru Dimca and Gabriel Sticlaru},
     title = {Hessian ideals of a homogeneous polynomial and generalized {Tjurina} algebras},
     journal = {Documenta mathematica},
     pages = {689--705},
     year = {2015},
     volume = {20},
     doi = {10.4171/dm/502},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/502/}
}
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