1986/01/01 by Robin Hartshorne · 4 citations
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Mathematics #Noether's theorem #Pure mathematics #Mathematical analysis #Lagrangian
paper · pdf · doi:10.1215/kjm/1250520873
openalex publication_date 1986/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/04/05
Recently while considering the possible special linear systems which can exist on a nonsingular plane curve, we rediscovered an old result of Max N o e th e r. The problem is to find the largest possible dimension of a linear system of degree d on a plane curve of degree k . The answer is that the linear systems of maximal dimension are the ones which "exist naturally" on the curve because of its plane embedding, namely the linear systems cut out by all plane curves of some other fixed degree, plus a few extra points or minus a few assigned base points. (See (2.1) for the exact statement.)