Currently I'm studying the article "Moduli of Enriques surfaces and Grothendieck-Riemann-Roch" by Pappas.See
I am particularly interested in how he applies the GRR.
Q1. What is meant by a "family of Enriques surfaces"? I was guessing a flat morphism $f:Y\longrightarrow T$ of smooth projective varieties such that each fibre is an Enriques surface, but maybe this is too general?
Q2. In the article it says that the higher direct images $R^i f_\ast O_Y$ are zero ($i>0$). Is this an application of Grauert's theorem (III.12, Cor. 12.9, Hartshorne)?
Q3. How to see easily that $R^0f_\ast O_Y = O_T$ ? I am guessing Grauert's theorem again.