Simple ramification point of a holomorphic map
= Simple ramification point of a holomorphic map
{title2=$e_p=2$}
A <ramification point> is simple when its <analytic ramification index> is two. Its contribution to <total ramification of a holomorphic map> is one. In suitable <local coordinates>, the <holomorphic map> is $t\mapsto t^2$; two nearby preimages merge there. A <ramification point> with $e_p=3$ contributes two even though it is just one point.