2007/01/15 by Kezheng Li, Li, Kezheng
Computer Science · Mathematics · #14G27 #14H05 #14H10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.math/0701407
openalex publication_date 2007/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \Cal C,\Cal C' be curves over a base scheme S with g(\Cal C)≥ 2. Then the functor T↦\generically smooth T-morphisms T×S\Cal C'→ T×S\Cal C\ from ((S-schemes)) to ((sets)) is represented by a quasi-finite unramified S-scheme. From this one can deduce that for any two integers g≥ 2 and g', there is an integer M(g,g') such that for any two curves C,C' over any field k with g(C)=g, g(C')=g', there are at most M(g,g') separable k-morphisms C'→ C. It is conjectured that the arithmetic function M(g,g') is bounded by a linear function of g'.