JournalsrlmVol. 32, No. 1pp. 63–78

On the infinitesimal Terracini Lemma

  • Ciro Ciliberto

    Università di Roma Tor Vergata, Italy
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In this paper we prove an infinitesimal version of the classical Terracini Lemma for 3-secant planes to a variety. Precisely we prove that if XPX \subseteq \mathcal P' is an irreducible, non-degenerate, projective complex variety of dimension nn with r3n+2r \geq 3n + 2, such that the variety of osculating planes to curves in XX has the expected dimension 3n3n and for every 0-dimensional, curvilinear scheme γ\gamma of length 3 contained in XX the family of hyperplanes sections of XX which are singular along γ\gamma has dimension larger that r3(n+1)r-3(n+1), then XX is 2-secant defective.

Cite this article

Ciro Ciliberto, On the infinitesimal Terracini Lemma. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 32 (2021), no. 1, pp. 63–78

DOI 10.4171/RLM/926