2016/02/20 by Jean–Marc Drézet, Drezet, Jean-Marc
Mathematics · Physics and Astronomy · #14B20 #14D20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1602.06386
openalex publication_date 2016/02/20 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
A primitive multiple curve is a Cohen-Macaulay irreducible projective curve Y\nthat can be locally embedded in a smooth surface, and such that C=Yred is\nsmooth. In this case, L=IC/IC2 is a line bundle on C. If Y is of\nmultiplicity 2, i.e. if IC2=0, Y is called a ribbon. If Y is a ribbon and\nh0(L-2)>0, then Y can be deformed to smooth curves, but in general a\ncoherent sheaf on Y cannot be deformed in coherent sheaves on the smooth\ncurves.\n A ribbon with associated line bundle L such that deg(L)=-d<0 can be deformed\nto reduced curves having 2 irreducible components if L can be written as\nL=OC(-P1-...-Pd), where P1,...,Pd are distinct points of C. In this case we\nprove that quasi locally free sheaves on Y can be deformed to torsion free\nsheaves on the reducible curves with two components. This has some consequences\non the structure and deformations of the moduli spaces of semi-stable sheaves\non Y.\n