Currently I'm studying the article "Moduli of Enriques surfaces and Grothendieck-Riemann-Roch" by Pappas. See

http://arxiv.org/PS_cache/math/pdf/0701/0701546v1.pdf

I am particularly interested in how he applies the GRR.

\textbf{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?

\textbf{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)?

\textbf{Q3.} How to see easily that $R^0f_\ast O_Y = O_T$ ? I am guessing Grauert's theorem again.

Currently I'm studying the article Moduli of Enriques surfaces and Grothendieck-Riemann-Roch by Pappas.

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.