2019/04/15 by Edoardo Ballico, Ballico, Edoardo, Claudio Fontanari +3
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Polynomial and algebraic computation #Primary 14C05 #Secondary 14H10 #math.AG #msc:14C05 #msc:14H10
paper · pdf · doi:10.48550/arxiv.1904.07716
Introductory section has been rewritten together with a historical remark concerning Severi's assertion on the Hilbert scheme of smooth curves. Some of main results have been stated precisely, especially on the existence part. Several typos corrected and references updated with some expository improvement. Final version. arXiv admin note: substantial text overlap with arXiv:1903.02307
openalex publication_date 2019/04/15 · openalex created_date 2019/04/25 · arxiv created 2019/06/29 · arxiv updated 2019/07/03 · openalex updated_date 2026/07/28
Let Hd,g,r be the Hilbert scheme parametrizing smooth irreducible and non-degenerate curves of degree d and genus g in \PPr. We denote by HLd,g,r the union of those components of Hd,g,r whose general element is linearly normal and we show that any non-empty HLd,g,r (d≥ g+r-3) is irreducible for an extensive range of triples (d,g,r) beyond the Brill-Noether range. This establishes the validity of a suitably modified assertion of Severi regarding the irreducibility of the Hilbert scheme HLd,g,r of linearly normal curves for g+r-3≤ d≤ g+r, r≥ 3, and g ≥ 2r+3 if d=g+r-3.