2
$\begingroup$

Let be $M$,$N$ and $X$ compact riemann surfaces, $f:M\to N$ an holomorphic map with ramifications points $\{p_1,\ldots,p_r\}$ with multiplicities $m_1,\ldots,m_r$ and, $g:X\to N$ holomorphic maps $\{q_1,\ldots,q_s\}$ with multiplicities $n_1,\ldots,n_s$. Now, let be $$Y\subset M\times X,~~~Y=\{(z,x)\in M\times X |~~f(z)=g(x) \}$$

My question: When $Y$ is a smooth riemann surface?

  • 0
    If $(x, y) \in M\times X$, then $y \in X$ so what do you mean by $f(y)$ given that $f : M \to X$?2012-12-17
  • 0
    In fact $f(y)=g(x)$2012-12-17
  • 0
    Now you have $f(y)$ with $y \in X$ but $f : M \to X$ and $g(x)$ with $x \in M$ but $g : N \to X$. Do you mean $Y = \{(x, y) \in M\times N\ |\ f(x) = g(y)\}$?2012-12-17
  • 0
    my apologies for the mess2012-12-17

1 Answers 1