In this paper we introduce some variation functions associated to the rank of the Infinitesimal Variations of Hodge Structure for a family of smooth projective complex curves. We give some bounds and inequalities and, in particular, we prove that if X is a smooth plane curve, then, there exists a first order deformation ξ∈ H^1(T_X) which deforms X as plane curve and such that ξ· : H^0(ω_X) → H^1(O_X) is an isomorphism. We also generalize the notions of variation functions to higher dimensional case and we analyze the link between IVHS and the weak and strong Lefschetz properties of the Jacobian ring of a smooth hypersurface.
Infinitesimal Variation Functions for Families of Smooth Varieties
Favale, Filippo Francesco;Pirola, Gian Pietro
2022-01-01
Abstract
In this paper we introduce some variation functions associated to the rank of the Infinitesimal Variations of Hodge Structure for a family of smooth projective complex curves. We give some bounds and inequalities and, in particular, we prove that if X is a smooth plane curve, then, there exists a first order deformation ξ∈ H^1(T_X) which deforms X as plane curve and such that ξ· : H^0(ω_X) → H^1(O_X) is an isomorphism. We also generalize the notions of variation functions to higher dimensional case and we analyze the link between IVHS and the weak and strong Lefschetz properties of the Jacobian ring of a smooth hypersurface.File in questo prodotto:
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