A numerical approach to proving projectivity

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We present a nonconstructive method which uses intersection numbers and linear space theory for proving the existence of projective embeddings of suitable algebraic schemes, and we apply it to establish Chevalley's conjecture that a complete nonsingular variety such that any finite number of points is contained in an open affine subset is projective.

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In memory of Guido Castelnuovo in the recurrence of the first centenary of his birth.

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Kleiman, S.L. A numerical approach to proving projectivity. Annali di Matematica 71, 323–330 (1966).

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  • Finite Number
  • Linear Space
  • Numerical Approach
  • Space Theory
  • Intersection Number