Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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DEPENDENT SUBSETS OF EMBEDDED PROJECTIVE VARIETIES

  • Received : 2019.05.31
  • Accepted : 2019.09.19
  • Published : 2020.07.31
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Abstract

Let X ⊂ ℙr be an integral and non-degenerate variety. Set n := dim(X). Let 𝜌(X)" be the maximal integer such that every zero-dimensional scheme Z ⊂ X smoothable in X is linearly independent. We prove that X is linearly normal if 𝜌(X)" ≥ 2⌈(r + 2)/2⌉ and that 𝜌(X)" < 2⌈(r + 1)/(n + 1)⌉, unless either n = r or X is a rational normal curve.

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Acknowledgement

The author was partially supported by MIUR and GNSAGA of INdAM (Italy).

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