The Michigan Mathematical Journal

Belyi's theorem for complete intersections of general type

Ariyan Javanpeykar

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Michigan Math. J., Volume 66, Issue 1 (2017), 85-97.

First available in Project Euclid: 3 March 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14D05: Structure of families (Picard-Lefschetz, monodromy, etc.) 14J10: Families, moduli, classification: algebraic theory 14E30: Minimal model program (Mori theory, extremal rays) 14H10: Families, moduli (algebraic)


Javanpeykar, Ariyan. Belyi's theorem for complete intersections of general type. Michigan Math. J. 66 (2017), no. 1, 85--97. doi:10.1307/mmj/1488510026.

Export citation


  • S. J. Arakelov, Families of algebraic curves with fixed degeneracies, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971), 1269–1293.
  • I. Bauer, F. Catanese, and F. Grunewald, Faithful actions of the absolute Galois group on connected components of moduli spaces, Invent. Math. 199 (2015), no. 3, 859–888.
  • M. C. Beltrametti and A. J. Sommese, The adjunction theory of complex projective varieties, de Gruyter Exp. Math., 16, Walter de Gruyter & Co., Berlin, 1995.
  • G. V. Belyĭ, Galois extensions of a maximal cyclotomic field, Izv. Akad. Nauk SSSR Ser. Mat. 43 (1979), no. 2, 267–276, 479.
  • O. Benoist, Espace de modules d'intersections complètes lisses, Ph.D. thesis.
  • C. Birkar, P. Cascini, C. D. Hacon, and J. McKernan, Existence of minimal models for varieties of log general type, J. Amer. Math. Soc. 23 (2010), no. 2, 405–468.
  • O. Debarre, Higher-dimensional algebraic geometry, Universitext, Springer-Verlag, New York, 2001.
  • P. Deligne, N. Katz, and N. M. Katz, Groupes de monodromie en géométrie algébrique. II, Séminaire de Géométrie Algébrique du Bois-Marie 1967–1969 (SGA 7 II), Lecture Notes in Math., 340, Springer-Verlag, Berlin–New York, 1973.
  • R. W. Easton and R. Vakil, Absolute Galois acts faithfully on the components of the moduli space of surfaces: a Belyi-type theorem in higher dimension, Int. Math. Res. Not. IMRN 20 (2007), Art. ID rnm080.
  • H. Flenner, The infinitesimal Torelli problem for zero sets of sections of vector bundles, Math. Z. 193 (1986), no. 2, 307–322.
  • E. Girondo and G. González-Diez, On complex curves and complex surfaces defined over number fields, Teichmüller theory and moduli problem, Ramanujan Math. Soc. Lect. Notes Ser., 10, pp. 247–280, Ramanujan Math. Soc., Mysore, 2010.
  • G. González-Diez, Variations on Belyi's theorem, Q. J. Math. 57 (2006), no. 3, 339–354.
  • G. González-Diez, Belyi's theorem for complex surfaces, Amer. J. Math. 130 (2008), no. 1, 59–74.
  • G. González-Diez and D. Torres-Teigell, Non-homeomorphic Galois conjugate Beauville structures on $\operatorname{PSL}(2,p)$, Adv. Math. 229 (2012), no. 6, 3096–3122.
  • A. Grothendieck, Revêtements étales et groupe fondamental. Fasc. II: Exposés 6, 8 à 11, Sémin. Géom. Algébr., 1960/61, Institut des Hautes Études Scientifiques, Paris, 1963.
  • C. D. Hacon, J. McKernan, and C. Xu, ACC for log canonical thresholds, Ann. of Math. (2) 180 (2014), no. 2, 523–571.
  • S. Kebekus and S. J. Kovács, The structure of surfaces and threefolds mapping to the moduli stack of canonically polarized varieties, Duke Math. J. 155 (2010), no. 1, 1–33.
  • S. Kobayashi and T. Ochiai, Meromorphic mappings onto compact complex spaces of general type, Invent. Math. 31 (1975), no. 1, 7–16.
  • B. Köck, Belyi's theorem revisited, Beitr. Algebra Geom. 45 (2004), no. 1, 253–265.
  • J. Kollár and T. Matsusaka, Riemann–Roch type inequalities, Amer. J. Math. 105 (1983), no. 1, 229–252.
  • J. Kollár and S. Mori, Birational geometry of algebraic varieties, Cambridge Tracts in Math., 134, Cambridge University Press, Cambridge, 1998, With the collaboration of, Clemens, C. H. and Corti, A., Translated from the 1998 Japanese original.
  • S. J. Kovács, Strong non-isotriviality and rigidity, Recent progress in arithmetic and algebraic geometry, Contemp. Math., 386, pp. 47–55, Amer. Math. Soc., Providence, RI, 2005.
  • S. J. Kovács, Subvarieties of moduli stacks of canonically polarized varieties: generalizations of Shafarevich's conjecture, Algebraic geometry–-Seattle 2005. Part 2, Proc. Sympos. Pure Math., 80, pp. 685–709, Amer. Math. Soc., Providence, RI, 2009.
  • S. Kovács and M. Lieblich, Erratum for boundedness of families of canonically polarized manifolds: a higher-dimensional analogue of Shafarevich's conjecture, Ann. of Math. (2) 173 (2011), no. 1, 585–617.
  • R. Lazarsfeld, Positivity in algebraic geometry. I, Ergeb. Math. Grenzgeb. (3), 48, Springer-Verlag, Berlin, 2004, Classical setting: line bundles and linear series.
  • A. N. Paršin, Algebraic curves over function fields, Dokl. Akad. Nauk SSSR 183 (1968), 524–526.
  • A. N. Paršin, Algebraic curves over function fields. I, Izv. Akad. Nauk SSSR Ser. Mat. 32 (1968), 1191–1219.
  • Z. Patakfalvi, Arakelov–Parshin rigidity of towers of curve fibrations, Math. Z. 278 (2014), no. 3–4, 859–892.
  • F. Peng, Rigidity of subfamilies of hypersurfaces in $\Bbb{P}\sp n$ with maximal length of Griffiths–Yukawa coupling, Sci. China Math. 57 (2014), no. 7, 1419–1426.
  • C. A. M. Peters, Rigidity for variations of Hodge structure and Arakelov-type finiteness theorems, Compos. Math. 75 (1990), no. 1, 113–126.
  • C. A. M. Peters and J. H. M. Steenbrink, Mixed Hodge structures, Ergeb. Math. Grenzgeb. (3), 52, Springer-Verlag, Berlin, 2008.
  • L. Schneps, Dessins d'enfants on the Riemann sphere, The Grothendieck theory of dessins d'enfants (Luminy, 1993), London Math. Soc. Lecture Note Ser., 200, pp. 47–77, Cambridge University Press, Cambridge, 1994.
  • C. T. Simpson, Harmonic bundles on noncompact curves, J. Amer. Math. Soc. 3 (1990), no. 3, 713–770.
  • C. T. Simpson, Higgs bundles and local systems, Publ. Math. Inst. Hautes Études Sci. 75 (1992), 5–95.
  • T. Szamuely, Galois groups and fundamental groups, Cambridge Stud. Adv. Math., 117, Cambridge University Press, Cambridge, 2009.
  • I. Tsai, Dominating the varieties of general type, J. Reine Angew. Math. 483 (1997), 197–219.
  • E. Viehweg and K. Zuo, On the isotriviality of families of projective manifolds over curves, J. Algebraic Geom. 10 (2001), no. 4, 781–799.
  • E. Viehweg and K. Zuo, Base spaces of non-isotrivial families of smooth minimal models, Complex geometry (Göttingen, 2000), pp. 279–328, Springer, Berlin, 2002.
  • E. Viehweg and K. Zuo, Discreteness of minimal models of Kodaira dimension zero and subvarieties of moduli stacks, Surveys in differential geometry, Vol. VIII (Boston, MA, 2002), Surv. Differ. Geom., VIII, pp. 337–356, Int. Press, Somerville, MA, 2003.
  • E. Viehweg and K. Zuo, Complex multiplication, Griffiths–Yukawa couplings, and rigidity for families of hypersurfaces, J. Algebraic Geom. 14 (2005), no. 3, 481–528.
  • E. Viehweg and K. Zuo, Numerical bounds for semi-stable families of curves or of certain higher-dimensional manifolds, J. Algebraic Geom. 15 (2006), no. 4, 771–791.
  • A. Weil, The field of definition of a variety, Amer. J. Math. 78 (1956), 509–524.
  • Y. Zhang, Rigidity for families of polarized Calabi–Yau varieties, J. Differential Geom. 68 (2004), no. 2, 185–222.