On Lange's Conjecture

1997/05/22 by Teixidor-i-Bigas, Montserrat
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.alg-geom/9705019

Abstract

Let C be an algebraic curve of genus g. Let E be a vector bundle of rank n and degree d. Consider among all subbundles F' of E of rank n' those of maximal degree d'. Then s_n'(E)= n'd-nd'≤ n'(n-n')g. If E is stable s_n'(E)>0 while if E is generic s_n'(E)≥ n'(n-n')(g-1) . The following statement was conjectured by Lange: If 0

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