Hi,

My question is related to Algebraic Surfaces. I have seen that we always consider K3 surfaces which are smooth, but I wonder how can we define a non-smooth K3 surface.

The problem I see is on the canonical bundle. So if we suppose $X$ is an algebraic surface ofer a field $K$ and suppose we hace that the singular divisor is normal crossing. Then we have logarithmic differentials. So I wonder if the definition of non-smooth K3 surface is the one that I am imagine, that is: $X$ is a $K3$ surface if $H^1(X, \mathfrak O_X)=0$ and $\Omega^2_X(log)$ is trivial...

Thanks.