Talk:Hurwitz space

Some copy-editiing

${\mathcal {H}}_{G,n}(K)\simeq \left\{Y{\overset {p}{\to }}\mathbb {P} _{K}^{1}{\text{ with }}{\begin{matrix}\operatorname {Aut} (Y,p)\simeq G,\\Y{\text{ geometrically connected curve}},\\p{\text{ étale outside }}n{\text{ points}}\end{matrix}}\right\}.$

I found the above in this article. It was not properly indented and I fixed that. Now I'm wondering: are all three of the lines to the right of "with" supposed to be included as the object of the preposition "with"? If so, this should be formatter differently, lest it be misunderstood. Maybe like this:

${\mathcal {H}}_{G,n}(K)\simeq Y{\overset {p}{{}\to {}}}\mathbb {P} _{K}^{1}{\text{ with }}\left\{{\begin{array}{l}\operatorname {Aut} (Y,p)\simeq G,\\Y{\text{ geometrically connected curve}},\\p{\text{ étale outside }}n{\text{ points.}}\end{array}}\right\}$

Notice also that here I've used a left-aligned array rather than a "matrix". I've also adjusted the horizontal spacing next to the arrow with the superscript "p" by putting {{}\to{}} where {\to} had appeared. And I've relocated the period at the end of the sentence.

And is the word "with" supposed to be a quantifier, meaning "for some Y"? Or is it like the word "where", explaining the notation? Michael Hardy (talk) 22:21, 27 May 2023 (UTC)

It was supposed to be the set of all morphisms from a geometrically connected smooth curve to the projective line, étale outside n points, whose automorphism group is isomorphic to G, hence the "outwards braces". I'm open to different suggestions since your reaction indicates to me that it's obviously not clear. Beranger Seguin (talk) 17:08, 3 July 2023 (UTC)