JournalsrlmVol. 29, No. 4pp. 689–709

On Green’s proof of the infinitesimal Torelli theorem for hypersurfaces

  • Luca Rizzi

    Università di Udine, Italy
  • Francesco Zucconi

    Università di Udine, Italy
On Green’s proof of the infinitesimal Torelli theorem for hypersurfaces cover
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Abstract

We prove an equivalence between the infinitesimal Torelli theorem for top forms on a hypersurface XX contained inside a Grassmannian and the theory of adjoint volume forms. More precisely, via this theory and a suitable generalization of Macaulay’s theorem we show that the differential of the period map vanishes on an infinitesimal deformation if and only if certain explicitly given twisted volume forms go in the generalized Jacobi ideal of XX via the cup product homomorphism.

Cite this article

Luca Rizzi, Francesco Zucconi, On Green’s proof of the infinitesimal Torelli theorem for hypersurfaces. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 29 (2018), no. 4, pp. 689–709

DOI 10.4171/RLM/829