I'm reading Fulton's algebraic curves and I don't know if I understood correctly this definition on the page 46:
What does the author mean by $f,g\in \Gamma_h(V)$ being of the same degree? Since $f$ and $g$ are equivalence classes of $\Gamma_h(V)$ we can write $f=f'+I(V)$ and $g=g'+I(V)$, where $f',g'\in k[X_1,\ldots,X_{n+1}]$. So, is he saying that $f'$ and $g'$ are forms of the same degree?
Thanks