On the variety of rational space curves

1997/10/30 by Ziv Ran, Z. Ran, Ran, Z.
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9710034

arxiv created 1997/10/30 · openalex publication_date 1997/10/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the locus of irreducible nonsingular rational curves of degree d Pn, n>2, meeting a generic collection of linear subspaces. When this locus is 0 (resp 1)- dimensional, we compute (recursively) its degree (resp. geometric genus). The method is completely elementary and similar to that of (alg-geom/9704004, alg-geom/9708013), where the case n=2 was considered.

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