TITLE: k3 surface as ramified double cover of $\mathbb{P}^2$
QUESTION [9 upvotes]: I read that one example of k3 surface is a double cover of $\mathbb{P}^2\mathbb{C}$ ramified over a sextic. My question is why a sextic? i believe that the sextic is isomorphic to the ramification divisor, but why is this? also how can i see that k3 surfaces realized this way are deformation equivalent? 
thank you

REPLY [22 votes]: Q1: Hurwitz formula + canonical divisor of $\mathbb P^2$.
Q2: Move the curve in $\mathbb P^2$.