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Article Dans Une Revue Annali dell'Universita di Ferrara Année : 2017

On the syzygies and Hodge theory of nodal hypersurfaces

Alexandru Dimca

Résumé

We give sharp lower bounds for the degree of the syzygies involving the partial derivatives of a homogeneous polynomial defining an even dimensional nodal hypersurface. This implies the validity of formulas due to M. Saito, L. Wotzlaw and the author for the graded pieces with respect to the Hodge filtration of the top cohomology of the hypersurface complement in many new cases. A classical result by Severi on the position of the singularities of a nodal surface in $\mathbb{P}^3$ is improved and applications to deformation theory of nodal surfaces are given.

Dates et versions

hal-00940157 , version 1 (31-01-2014)

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Alexandru Dimca. On the syzygies and Hodge theory of nodal hypersurfaces. Annali dell'Universita di Ferrara, 2017, 63, pp.87-101. ⟨10.1007/s11565-017-0278-y⟩. ⟨hal-00940157⟩
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