Connections and the Second Main Theorem for Holomorphic Curves

2011/03/30 by Junjiro Noguchi, Noguchi, Junjiro
Mathematics · #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #Primary 32H30 #Scondary 30D35 #math.AG #math.CV #msc:30D35 #msc:32H30

paper · pdf · doi:10.48550/arxiv.1103.5819

21 pages

arxiv created 2011/03/30 · arxiv updated 2011/03/31

Abstract

By means of C^∞-connections we will prove a general second main theorem and some special ones for holomorphic curves. The method gives a geometric proof of H. Cartan's second main theorem in 1933. By applying the same method, we will prove some second main theorems in the case of the product space (\pone)² of the Riemann sphere.

Related

• Holomorphic projective connections on surfaces
• On a General Form of the Second Main Theorem
• The works of Charles Ehresmann on connections: from Cartan connections to connections on fibre bundles
• On connections on principal bundles
• H. Cartan's theory for Riemann surfaces