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==Examples==
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|last1=Hauser|first1=Herwig|last2=Lipman|first2=Joseph|last3=Oort|first3=Frans|coauthors=Adolfo Quirós|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|url=http://books.google.com/books?id=ByTyBwAAQBAJ&pg=PA83|accessdate=22 August 2017|date=2012-12-06|publisher=Birkhäuser|isbn=9783034883993|page=83}}</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>[https://web.math.princeton.edu/~kollar/book/modbook20170720.pdf ''Moduli of Surfaces'', draft (PDF)] at p. 11</ref> Braungardt has posed the question whether [[Belyi's theorem]] 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>[https://01416e54-a-62cb3a1a-s-sites.googlegroups.com/site/wushijig/unifyingthemessuggestedbybelyistheoremseptember2009.pdf?attachauth=ANoY7cpkNGR-KDdDjRekRK7MEadxsUUvCndH6yK-itIDzVXBvjDrJQ46EEXIqOk_jqOIrF8r0Q7_Y2Rbk87bgDvJweodlyBDh33pxldtHWsF0M4AdbQRbdIYnHEfPINbeAA69lnICUcYqSmxUVTRlDxSNo9F7Gi6pd8D4nbiLcvWGuDBWrVxh_fCgTIgQglpLUOPONgnR1itnIEaVQfrsfndpvZy2bNco9-Sw8c6zreXDR138DLMUGeUwiK25e6BbeP33swnshqx&attredirects=0 Wushi Goldring, ''Unifying Themes Suggested by Belyi’s Theorem'' (PDF)] at p. 22</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=Bloch|first=Spencer|title=Algebraic Geometry: Bowdoin 1985|url=http://books.google.com/books?id=50IECAAAQBAJ&pg=PA103|accessdate=22 August 2017|year=1987|publisher=American Mathematical Soc.|isbn=9780821814802|page=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|last1=Greuel|first1=Gert-Martin|last2=Trautmann|first2=Günther|title=Singularities, Representation of Algebras, and Vector Bundles: Proceedings of a Symposium held in Lambrecht/Pfalz, Fed.Rep. of Germany, Dec. 13-17, 1985|url=http://books.google.com/books?id=Ukh6CwAAQBAJ&pg=PA336|accessdate=22 August 2017|date=2006-11-15|publisher=Springer|isbn=9783540478515|page=336}}</ref>
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