The local cohomology of the Jacobian ring
Copyright policy )The local cohomology of the Jacobian ring
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)) .
- Roma Tre University Italy
Macaulay's theorem, arrangements of hyperplanes, 14B15, Local complex singularities, Jacobian ideal, logarithmic differential forms, stable vector bundles, LOCAL COHOMOLOGY; HYPERSURFACE; LOGARITHMIC DIFFERENTIAL, hypersurfaces, local cohomology, Torelli type theorems, free divisors, Mathematics - Algebraic Geometry, Torelli problem, Mixed Hodge theory of singular varieties (complex-analytic aspects), Local cohomology and algebraic geometry, FOS: Mathematics, Hypersurfaces and algebraic geometry, Algebraic Geometry (math.AG), Hodge decomposition, logarithmic vector fields
Macaulay's theorem, arrangements of hyperplanes, 14B15, Local complex singularities, Jacobian ideal, logarithmic differential forms, stable vector bundles, LOCAL COHOMOLOGY; HYPERSURFACE; LOGARITHMIC DIFFERENTIAL, hypersurfaces, local cohomology, Torelli type theorems, free divisors, Mathematics - Algebraic Geometry, Torelli problem, Mixed Hodge theory of singular varieties (complex-analytic aspects), Local cohomology and algebraic geometry, FOS: Mathematics, Hypersurfaces and algebraic geometry, Algebraic Geometry (math.AG), Hodge decomposition, logarithmic vector fields
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