2001/07/16 by Luis Fuentes Garcia, Luis Fuentes García, Garcia, Luis Fuentes +3
Mathematics · #14H25 #14H45 #14J26 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Primary #Secondary #math.AG #msc:14H25 #msc:14H45 #msc:14J26
paper · pdf · doi:10.48550/arxiv.math/0107114
Latex2.09; 32 pages
openalex publication_date 2001/07/16 · arxiv created 2002/04/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove the existence of canonical scrolls; that is, scrolls playing the role of canonical curves. First of all, they provide the geometrical version of Riemann Roch Teorem: any special scroll is the projection of a canonical scroll and they allow to understand the classification of special scrolls in P3. Canonical scrolls correspond to the projective model of canonical geometrically ruled surfaces over a smooth curve. We also prove that the generic canonical scroll is projectively normal except in the hyperelliptic case and for very particular cases in the nonhyperelliptic situation.