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Mumford proved that if ''g'' > 1, there exists a coarse moduli scheme of smooth curves of genus ''g'', which is [[quasi-projective]].<ref>{{cite book |chapter=10.4 Coarse moduli schemes |chapter-url=https://books.google.com/books?id=ByTyBwAAQBAJ&pg=PA83|title=Resolution of Singularities: A research textbook in tribute to Oscar Zariski Based on the courses given at the Working Week in Obergurgl, Austria, September 7–14, 1997|last1=Hauser|first1=Herwig|last2=Lipman|first2=Joseph|last3=Oort|first3=Frans|last4=Quirós|first4=Adolfo|date=2012-12-06|publisher=Birkhäuser|isbn=9783034883993|page=83|access-date=22 August 2017}}</ref> According to a recent survey by [[János Kollár]], it "has a rich and intriguing intrinsic geometry which is related to major questions in many branches of mathematics and theoretical physics."<ref>{{cite book |first=János |last=Kollár |chapter=1.1. Short History Of Moduli Problems: Theorem 1.14 |title=Families of varieties of general type |date=July 20, 2017 |pages=11 |url=https://web.math.princeton.edu/~kollar/book/modbook20170720.pdf }}</ref> Braungardt has posed the question whether [[Belyi's theorem]] can be generalised to varieties of higher dimension over the [[field of algebraic numbers]], with the formulation that they are generally birational to a finite [[étale covering]] of a moduli space of curves.<ref>{{cite book |first=W. |last=Goldring |chapter=Unifying themes suggested by Belyi’s Theorem |chapter-url= |title=Number Theory, Analysis and Geometry |publisher=Springer |date=2012 |isbn=978-1-4614-1260-1 |pages=181–214 See p. 203|doi=10.1007/978-1-4614-1260-1_10}}</ref>
Using the notion of [[stable vector bundle]], coarse moduli schemes for the vector bundles on any smooth [[complex variety]] have been shown to exist, and to be quasi-projective: the statement uses the concept of [[semistable vector bundle|semistability]].<ref>{{cite book|last=Harris |first=Joe |title=Algebraic Geometry: Bowdoin 1985 |chapter=Curves and their moduli |chapter-url=https://books.google.com/books?id=50IECAAAQBAJ&pg=PA103 |year=1987|publisher=American Mathematical Soc.|isbn=978-0-8218-1480-2 |pages=99–143 See p. 103}}</ref> It is possible to identify the coarse moduli space of special [[instanton bundle]]s, in mathematical physics, with objects in the classical geometry of conics, in certain cases.<ref>{{cite book |first1=W. |
==References==
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