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Moduli space
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=== Research articles === ==== Fundamental papers ==== *{{Cite journal | last = Grothendieck | first = Alexander | author-link = Alexander Grothendieck | title = Techniques de construction en géométrie analytique. I. Description axiomatique de l'espace de Teichmüller et de ses variantes. | place = Paris | year = 1960–1961 | journal = Séminaire Henri Cartan 13 No. 1, Exposés No. 7 and 8 | url = http://archive.numdam.org/article/SHC_1960-1961__13_1_A4_0.pdf }} * [[David Mumford|Mumford, David]], ''Geometric invariant theory''. [[Ergebnisse der Mathematik und ihrer Grenzgebiete]], Neue Folge, Band 34 Springer-Verlag, Berlin-New York 1965 vi+145 pp {{MathSciNet|id=0214602}} * Mumford, David; Fogarty, J.; Kirwan, F. ''Geometric invariant theory''. Third edition. Ergebnisse der Mathematik und ihrer Grenzgebiete (2) (Results in Mathematics and Related Areas (2)), 34. Springer-Verlag, Berlin, 1994. xiv+292 pp. {{MathSciNet|id=1304906}} {{isbn|3-540-56963-4}} ==== Early applications ==== *{{cite journal | last = Deligne | first = Pierre | author-link = Pierre Deligne |author2=Mumford, David | title = The irreducibility of the space of curves of given genus | journal = Publications Mathématiques de l'IHÉS | volume = 36 | pages = 75–109 | year = 1969 | issue = 1 | url = http://archive.numdam.org/article/PMIHES_1969__36__75_0.pdf | doi =10.1007/bf02684599 | citeseerx = 10.1.1.589.288 }} *{{cite book | last1 = Faltings | first1 = Gerd | author-link = Gerd Faltings | last2=Chai | first2=Ching-Li | title = Degeneration of Abelian Varieties | publisher = Springer-Verlag | year = 1990 | location = Berlin | series = Ergebnisse der Mathematik und ihrer Grenzgebiete | volume = 22 | others = With an appendix by David Mumford | mr = 1083353 | doi = 10.1007/978-3-662-02632-8 | isbn =978-3-540-52015-3 }} *{{cite book | last1 = Katz | first1 = Nicholas M | last2=Mazur | first2=Barry |author-link2=Barry Mazur | title = Arithmetic Moduli of Elliptic Curves | publisher = [[Princeton University Press]] | series = Annals of Mathematics Studies | volume = 108 | year = 1985 | mr = 772569 | isbn =978-0-691-08352-0 }} ==== Other references ==== * Papadopoulos, Athanase, ed. (2007), Handbook of Teichmüller theory. Vol. I, IRMA Lectures in Mathematics and Theoretical Physics, 11, European Mathematical Society (EMS), Zürich, {{doi|10.4171/029}}, {{isbn|978-3-03719-029-6}}, {{MR|2284826}} * Papadopoulos, Athanase, ed. (2009), Handbook of Teichmüller theory. Vol. II, IRMA Lectures in Mathematics and Theoretical Physics, 13, European Mathematical Society (EMS), Zürich, {{doi|10.4171/055}}, {{isbn|978-3-03719-055-5}}, {{MR|2524085}} * Papadopoulos, Athanase, ed. (2012), Handbook of Teichmüller theory. Vol. III, IRMA Lectures in Mathematics and Theoretical Physics, 17, European Mathematical Society (EMS), Zürich, {{doi|10.4171/103}}, {{isbn|978-3-03719-103-3}}. ==== Other articles and sources ==== *{{cite book | last1 = Harris | first1 = Joe | author-link = Joe Harris (mathematician) | last2 = Morrison | first2 = Ian | title = Moduli of Curves | publisher = [[Springer Verlag]] | year = 1998 | location = New York | mr = 1631825 | doi = 10.1007/b98867 | volume = 187 | series = Graduate Texts in Mathematics | isbn =978-0-387-98429-2 }} *{{cite book | last = Viehweg | first = Eckart | author-link = Eckart Viehweg | title = Quasi-Projective Moduli for Polarized Manifolds | publisher = Springer Verlag | year = 1995 | url = http://www.uni-due.de/%7Emat903/books/vibuch.pdf | isbn =978-3-540-59255-6 }} *{{cite journal | last = Simpson | first = Carlos | title = Moduli of representations of the fundamental group of a smooth projective variety I | journal = Publications Mathématiques de l'IHÉS | volume = 79 | pages = 47–129 | year = 1994 | issue = 1 | url = http://archive.numdam.org/article/PMIHES_1994__79__47_0.pdf | doi =10.1007/bf02698887 }} *[[Maryam Mirzakhani]] (2007) [https://www.math.stonybrook.edu/~mlyubich/Archive/Geometry/Teichmuller%20Space/Mirz3.pdf "Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces"] [[Inventiones Mathematicae]]
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