On the number of coincidences of morphisms between closed Riemann surfaces (Q1325604)

The authors show that for two distinct holomorphic maps \(f_ 1, f_ 2: M\to M'\) between Riemann surfaces the number of points (counted with multiplicity) in which the two maps agree is less than or equal to \(d_ 1+ 2g' \sqrt {d_ 1 d_ 2} +d_ 2\), where \(d_ i\) is the degree of \(f_ i\), \(i=1,2\), and \(g'\) is the genus of \(M'\). The proof makes use of a suitable version of Lefschetz' trace formula.