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I would like to know what the "Igusa model" of the modular curve is and basic properties about it.

Can someone point me to a reference?

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Are you talking about "Igusa curves" - the special modular curves that occur in positive characteristic? – Ramsey Mar 21 2012 at 18:35
I am not sure. I saw this term, for instance, in a paper by Winnie Li called "Modularity of Asymptotically Optimal Towers of Function Fields" (p. 10). – expmat Mar 21 2012 at 19:15
I don't have access to the paper at the moment. At the risk of suggesting something obvious, perhaps there are references in the bibliography that will help. If elliptic curves in positive characteristic or modular forms modulo a prime $p$ are relevant to the paper, then Igusa curves may be what is meant. One reference for these curves is Katz-Mazur - "Arithmetic moduli of elliptic curves." – Ramsey Mar 21 2012 at 22:38
This book (books.google.ca/…) and this pdf are the closest references I could find (collectionscanada.gc.ca/obj/s4/f2/dsk3/ftp04/…). – Eugene May 12 2012 at 3:18

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