Maybe this question is not suitable for this platform, I already put that same question in math.stackexchange and I find only vague answers. 


I'm studying the book of Rick Miranda; Algebraic Curves and Riemann Surfaces. I'm studying about degree of projective curves and I find a term used very often and that is very important by the amount of times it appears:


"general hyperplane $H$ in $\mathbb{P}^n$"


I need to understand what this means, but in the context of the subject. I searched all over Rick Miranda's book, but I could not find it. 


I read Geometry of Algebraic Curves-Volume I, I often encounter the placement "Let $H$ be a general hyperplane in $\mathbb{P}^n$. 


Important facts follow from this fact, as for example the calculus of the degree of the map of Gauss constructed from the divisor theta, for the demonstration of the Theorem of Torelli.


So it may seem trivial, but it's quite important the meaning of: 


"general hyperplane $H$ in $\mathbb{P}^n$". 


It turns out that I can not find it in any book. Everyone just uses it, but I need to know. So I am also grateful for references.


Thank you! 



Meaning of general hyperplane $H$ in $\mathbb{P}^n$
The sentence:



> 
> Let $H$ be a general hyperplane. Then do so and so... 
> 
> 
> 


Means:



> 
> Pick a hyperplane $H$. Then do so and so, while keeping in mind that the "so and so" might sometimes not work out/be false/be impossible to do.
> 
> 
> 


The use of the word *general* means that the *set of hyperplanes $H$* for which "so and so" works/is true/is possible to do is *Zariski-open* [edit: and *non-empty!*] (or contains a non-empty Zariski-open subset) inside the set of all hyperplanes.


