2009/05/12 by Eduardo Esteves, Esteves, Eduardo, Patrícia Nogueira +2
Computer Science · Mathematics · #14D06 #14H10 #14H55 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14D06 #msc:14H10 #msc:14H55
paper · pdf · doi:10.48550/arxiv.0905.1824
30 pages
arxiv created 2009/05/12 · openalex publication_date 2009/05/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let C be a projective Gorenstein curve over an algebraically closed field of characteristic 0. A generalized linear system on C is a pair (I,f) consisting of a torsion-free, rank-1 sheaf I on C and a map of vector spaces f to the space of global sections of I. If the system is nondegenerate on every irreducible component of C, we associate to it a 0-cycle W, its Weierstrass cycle. Then we show that for each one-parameter family of curves C(t) degenerating to C, and each family of linear systems (L(t),f(t)) along C(t), with L(t) invertible, degenerating to (I,f), the corresponding Weierstrass divisors degenerate to a subscheme whose associated 0-cycle is W. We show that the limit subscheme contains always an "intrinsic" subscheme, canonically associated to (I,f), but the limit itself depends on the family L(t).