Classification of Algebraic Space Curves, III

Robin Hartshorne

Chapter 5 in Algebraic Geometry and its Applications, 1994, pp 113-120 from Springer

Abstract: Abstract Over a fixed algebraically closed ground field k, we consider irreducible non-singular projective curves in the projective space P k 3 . The original classification problem for algebraic space curves could be described as finding all such curves, giving their numerical invariants, and determining the algebraic families they belong to. This was the problem tackled in the great treatises of M. Noether [10] and G. Halphen [5] over a hundred years ago, and has been the subject of numerous investigations since then. The determination of which pairs can occur as the degree and genus of a non-singular space curve was stated by Halphen, but only properly proved within the last decade by Gruson and Peskine [4]. Now it is reasonable to ask for finer numerical data, for example one can ask for the postulation of all possible curves, which means for each n, the number of conditions for a hypersurface of degree n to contain the curve.

Keywords: Irreducible Component; Hilbert Scheme; Arithmetic Genus; Numerical Invariant; Numerical Character (search for similar items in EconPapers)
Date: 1994
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DOI: 10.1007/978-1-4612-2628-4_5

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