Geodesic
The local cohomology of the Jacobian ring
Documenta mathematica, Tome 19 (2014), pp. 541-565.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study the 0-th local cohomology module $H^0_{\mathbf{m}}(R(f))$ of the jacobian ring $R(f)$ of a singular reduced complex projective hypersurface $X$, by relating it to the sheaf of logarithmic vector fields along $X$. We investigate the analogies between $H^0_{\mathbf{m}}(R(f))$ and the well known properties of the jacobian ring of a nonsingular hypersurface. In particular we study self-duality, Hodge theoretic and Torelli type questions for $H^0_{\mathbf{m}}(R(f))$.
Classification : 14B15 
@article{DOCMA_2014__19__a28,
     author = {Sernesi, Edoardo},
     title = {The local cohomology of the {Jacobian} ring},
     journal = {Documenta mathematica},
     pages = {541--565},
     publisher = {mathdoc},
     volume = {19},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a28/}
}
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Sernesi, Edoardo. The local cohomology of the Jacobian ring. Documenta mathematica, Tome 19 (2014), pp. 541-565. http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a28/