Geodesic
The local cohomology of the Jacobian ring
Documenta mathematica, Tome 19 (2014), pp. 541-565
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We study the 0-th local cohomology module Hm0​(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 Hm0​(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 Hm0​(R(f)).
DOI : 10.4171/dm/455
Classification : 14B15 
@article{10_4171_dm_455,
     author = {Edoardo Sernesi},
     title = {The local cohomology of the {Jacobian} ring},
     journal = {Documenta mathematica},
     pages = {541--565},
     year = {2014},
     volume = {19},
     doi = {10.4171/dm/455},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/455/}
}
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Edoardo Sernesi. The local cohomology of the Jacobian ring. Documenta mathematica, Tome 19 (2014), pp. 541-565. doi: 10.4171/dm/455

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