On tangential deformations of homogeneous polynomials

DOI10.1002/MANA.201600531zbMATH Open1454.14027arXiv1505.00615OpenAlexW2583539968MaRDI QIDQ4598753

Zhenjian Wang

Publication date: 15 December 2017

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Abstract: The Jacobian ideal provides the set of infinitesimally trivial deformations for a homogeneous polynomial, or for the corresponding complex projective hypersurface. In this article, we investigate whether the associated linear deformation is indeed trivial, and show that the answer is no in a general situation. We also give a characterization of tangentially smoothable hypersurfaces with isolated singularities. Our results have applications in the local study of variations of projective hypersurfaces, complementing the global versions given by J. Carlson and P. Griffiths, R. Donagi and the author, and in the study of isotrivial linear systems on the projective space, showing that a general divisor does not belong to an isotrivial linear system of positive dimension.

Full work available at URL: https://arxiv.org/abs/1505.00615

zbMATH Keywords

tangential deformationtangential smoothabilitytotally tangentially unstable

Mathematics Subject Classification ID

Hypersurfaces and algebraic geometry (14J70) Deformations of singularities (14B07) Formal methods and deformations in algebraic geometry (14D15) Torelli problem (14C34)

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