Must the top of a sukkah be level?

Question

I saw this question about a portable sukkah and I immediately thought of those pop-up canopies that you sometimes see at picnics and the like. The canopy has a metal or plastic frame that folds up and a (usually plastic) cover over the top. I've seen ones where the cover can be removed.

This seems like a reasonable basis for a portable sukkah except for one thing: these canopies have a peak in the center (to shed rain). That would make it difficult to have the s'chach level with the ground:

And that made me wonder:
Is the s'chach required to be level?
Or is a sukkah allowed to have a peaked or pointed roof?

Assume, for purposes of this question, kosher supporting materials and a means of attaching s'chach to a slanted frame; I'm just asking about the legality of the shape.

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(A similar question arises with a palapa, a temporary structure with a convex roof but does not question the validity of the slanted roof rather the validity of the structure itself if perched in a place that will destroy the succcah e.g sea shore.)

Answer 1

This is addressed in Shulchan Aruch Orach Chaim 631,10:

סוכה שאין לה גג כגון שהיו ראשי הדפנות דבוקות זו בזו כמין צריף או שסמך ראש הדופן של סוכה לכותל פסולה ואם היה לה גג אפילו טפח או שהגביה הדופן הסמוך לכותל מן הקרקע טפח הרי זו כשרה. הגה: וצריך שיהיה בה שבעה טפחים על שבעה בגובה עשרה טפחים (טור)
A Succah without a flat roof at all e.g the entire walls slant and meet in the middle like a tent, alternatively one wall is slanted against a straight wall is Invalid. But if there was a section of roof flat roof even a Tefach (Hand-breadth )alternatively the slanted wall(s) rested on a vertical wall with a length of a tefach form the ground this is Kosher. Rema: But we need a volume of 7 by 7 tefachim with a height of 10 tefachim within these slanted walls (that have a tefach horizontal roof with sechach or vertical wall).

So yes your gazebo has straight walls much larger than 1 tefach (and the volume of a gazebo is much larger than 7x7x10), so putting the Sechach on the slanted sections of the roof makes it Kosher with 3 walls.