Hi, this is more or less a "reference" question.

Suppose $D$ a redueced irreducibile divisor in $X$ and I take $f:Y\rightarrow D$ a desingularization of his.

What information can i get from the support of the higher direct imagese $R^if_*\mathcal{O}_Y$?

for example if they are all empty then the divisor has rational singularities. If the codim of $R^1f_*\mathcal{O}_Y$ in $X$ is greater than 3 then the divisor is normal

I know this question is a little bit vague, but I really do not know where to find information of this kind

thank you for your help