Let V :f=0 be a hypersurface of degreed≥3 in the complex projective space P^n,n≥3,having only isolated singularities.Let M(f) be the associatedJ Jacobian algebra and H:ℓ=0 be a hyperplane in P^n avoiding the singularities of V, but such that V∩H is singular.We related the Lefschetz type properties of the linear maps ℓ:M(f)_k→M(f)_k+1induced by the multiplication by linearf orm ℓ to the singularities of the hyperplane section V∩H.Similar results are obtained for the Jacobian module N(f).
Lefschetz properties of Jacobian algebras and Jacobian modules / Dimca, A., Ilardi, G.. - In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE. - ISSN 2036-2145. - Vol. XXVI (2025):5(2025), pp. 1603-1616. [10.2422/2036-2145.202301_014]
Lefschetz properties of Jacobian algebras and Jacobian modules
G. Ilardi
2025
Abstract
Let V :f=0 be a hypersurface of degreed≥3 in the complex projective space P^n,n≥3,having only isolated singularities.Let M(f) be the associatedJ Jacobian algebra and H:ℓ=0 be a hyperplane in P^n avoiding the singularities of V, but such that V∩H is singular.We related the Lefschetz type properties of the linear maps ℓ:M(f)_k→M(f)_k+1induced by the multiplication by linearf orm ℓ to the singularities of the hyperplane section V∩H.Similar results are obtained for the Jacobian module N(f).| File | Dimensione | Formato | |
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