Euler and algebraic geometry
HTML articles powered by AMS MathViewer
- by Burt Totaro PDF
- Bull. Amer. Math. Soc. 44 (2007), 541-559
References
- Yves André, $G$-functions and geometry, Aspects of Mathematics, E13, Friedr. Vieweg & Sohn, Braunschweig, 1989. MR 990016, DOI 10.1007/978-3-663-14108-2
- Yves AndrĂ© and Francesco Baldassarri, Geometric theory of $G$-functions, Arithmetic geometry (Cortona, 1994) Sympos. Math., XXXVII, Cambridge Univ. Press, Cambridge, 1997, pp. 1â22. MR 1472489
- Arnaud Beauville, Les familles stables de courbes elliptiques sur $\textbf {P}^{1}$ admettant quatre fibres singuliĂšres, C. R. Acad. Sci. Paris SĂ©r. I Math. 294 (1982), no. 19, 657â660 (French, with English summary). MR 664643
- Bassem Ben Hamed and Lubomir Gavrilov, Families of PainlevĂ© VI equations having a common solution, Int. Math. Res. Not. 60 (2005), 3727â3752. MR 2205113, DOI 10.1155/IMRN.2005.3727 BCHM C. Birkar, P. Cascini, C. Hacon, and J. McKernan. Existence of minimal models for varieties of log general type. arXiv:math.AG/0610203
- Philip Boalch, From Klein to PainlevĂ© via Fourier, Laplace and Jimbo, Proc. London Math. Soc. (3) 90 (2005), no. 1, 167â208. MR 2107041, DOI 10.1112/S0024611504015011
- Philip Candelas, Xenia C. de la Ossa, Paul S. Green, and Linda Parkes, A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory, Nuclear Phys. B 359 (1991), no. 1, 21â74. MR 1115626, DOI 10.1016/0550-3213(91)90292-6
- James Carlson, Stefan MĂŒller-Stach, and Chris Peters, Period mappings and period domains, Cambridge Studies in Advanced Mathematics, vol. 85, Cambridge University Press, Cambridge, 2003. MR 2012297
- Antoine Chambert-Loir, ThĂ©orĂšmes dâalgĂ©bricitĂ© en gĂ©omĂ©trie diophantienne (dâaprĂšs J.-B. Bost, Y. AndrĂ©, D. & G. Chudnovsky), AstĂ©risque 282 (2002), Exp. No. 886, viii, 175â209 (French, with French summary). SĂ©minaire Bourbaki, Vol. 2000/2001. MR 1975179
- D. V. Chudnovsky and G. V. Chudnovsky, Applications of PadĂ© approximations to the Grothendieck conjecture on linear differential equations, Number theory (New York, 1983â84) Lecture Notes in Math., vol. 1135, Springer, Berlin, 1985, pp. 52â100. MR 803350, DOI 10.1007/BFb0074601 CS K. Corlette and C. Simpson. On the classification of rank two representations of quasiprojective fundamental groups. arXiv:math.AG/0702287 Corti A. Corti, ed. Flips for 3-folds and 4-folds. Oxford (2007).
- Pierre Deligne, Ăquations diffĂ©rentielles Ă points singuliers rĂ©guliers, Lecture Notes in Mathematics, Vol. 163, Springer-Verlag, Berlin-New York, 1970 (French). MR 0417174, DOI 10.1007/BFb0061194
- Boris Dubrovin, PainlevĂ© transcendents in two-dimensional topological field theory, The PainlevĂ© property, CRM Ser. Math. Phys., Springer, New York, 1999, pp. 287â412. MR 1713580
- B. Dubrovin and M. Mazzocco, Monodromy of certain PainlevĂ©-VI transcendents and reflection groups, Invent. Math. 141 (2000), no. 1, 55â147. MR 1767271, DOI 10.1007/PL00005790
- Bernard Dwork, Giovanni Gerotto, and Francis J. Sullivan, An introduction to $G$-functions, Annals of Mathematics Studies, vol. 133, Princeton University Press, Princeton, NJ, 1994. MR 1274045 Eulerrat L. Euler. Solutio generalis quorundam problematum Diophanteorum quae vulgo nonnisi solutiones speciales admittere videntur. Leonhardi Euleri opera omnia, v. 1, pt. 2, 428â458. Teubner (1915).
- Leonhard Euler, Einleitung in die Analysis des Unendlichen. Teil 1, Springer-Verlag, Berlin, 1983 (German). Reprint of the 1885 edition; With an introduction by Wolfgang Walter. MR 715928, DOI 10.1007/978-3-662-02338-9
- Jean-Marc Fontaine and Barry Mazur, Geometric Galois representations, Elliptic curves, modular forms, & Fermatâs last theorem (Hong Kong, 1993) Ser. Number Theory, I, Int. Press, Cambridge, MA, 1995, pp. 41â78. MR 1363495
- Wiliam M. Goldman and Walter D. Neumann, Homological action of the modular group on some cubic moduli spaces, Math. Res. Lett. 12 (2005), no. 4, 575â591. MR 2155233, DOI 10.4310/MRL.2005.v12.n4.a11
- Phillip A. Griffiths, Periods of integrals on algebraic manifolds: Summary of main results and discussion of open problems, Bull. Amer. Math. Soc. 76 (1970), 228â296. MR 258824, DOI 10.1090/S0002-9904-1970-12444-2 HST M. Harris, N. Shepherd-Barron, and R. Taylor. A family of Calabi-Yau varieties and potential automorphy. Preprint (2006).
- N. J. Hitchin, Poncelet polygons and the PainlevĂ© equations, Geometry and analysis (Bombay, 1992) Tata Inst. Fund. Res., Bombay, 1995, pp. 151â185. MR 1351506
- Rolf-Peter Holzapfel, Geometry and arithmetic around Euler partial differential equations, Mathematics and its Applications (East European Series), vol. 11, D. Reidel Publishing Co., Dordrecht, 1986. MR 867406
- Kentaro Hori, Sheldon Katz, Albrecht Klemm, Rahul Pandharipande, Richard Thomas, Cumrun Vafa, Ravi Vakil, and Eric Zaslow, Mirror symmetry, Clay Mathematics Monographs, vol. 1, American Mathematical Society, Providence, RI; Clay Mathematics Institute, Cambridge, MA, 2003. With a preface by Vafa. MR 2003030
- Dale Husemöller, Elliptic curves, 2nd ed., Graduate Texts in Mathematics, vol. 111, Springer-Verlag, New York, 2004. With appendices by Otto Forster, Ruth Lawrence and Stefan Theisen. MR 2024529
- Katsunori Iwasaki, Hironobu Kimura, Shun Shimomura, and Masaaki Yoshida, From Gauss to Painlevé, Aspects of Mathematics, E16, Friedr. Vieweg & Sohn, Braunschweig, 1991. A modern theory of special functions. MR 1118604, DOI 10.1007/978-3-322-90163-7
- Nicholas M. Katz, Nilpotent connections and the monodromy theorem: Applications of a result of Turrittin, Inst. Hautes Ătudes Sci. Publ. Math. 39 (1970), 175â232. MR 291177, DOI 10.1007/BF02684688
- Nicholas M. Katz, Algebraic solutions of differential equations ($p$-curvature and the Hodge filtration), Invent. Math. 18 (1972), 1â118. MR 337959, DOI 10.1007/BF01389714
- Nicholas M. Katz, Rigid local systems, Annals of Mathematics Studies, vol. 139, Princeton University Press, Princeton, NJ, 1996. MR 1366651, DOI 10.1515/9781400882595 KF F. Klein and R. Fricke. Vorlesungen ĂŒber die Theorie der elliptischen Modulfunktionen, v. 1. Teubner (1890).
- JĂĄnos KollĂĄr, Karen E. Smith, and Alessio Corti, Rational and nearly rational varieties, Cambridge Studies in Advanced Mathematics, vol. 92, Cambridge University Press, Cambridge, 2004. MR 2062787, DOI 10.1017/CBO9780511734991
- Maxim Kontsevich and Don Zagier, Periods, Mathematics unlimitedâ2001 and beyond, Springer, Berlin, 2001, pp. 771â808. MR 1852188
- Shigefumi Mori, Flip theorem and the existence of minimal models for $3$-folds, J. Amer. Math. Soc. 1 (1988), no. 1, 117â253. MR 924704, DOI 10.1090/S0894-0347-1988-0924704-X
- Miles Reid, Twenty-five years of $3$-foldsâan old personâs view, Explicit birational geometry of 3-folds, London Math. Soc. Lecture Note Ser., vol. 281, Cambridge Univ. Press, Cambridge, 2000, pp. 313â343. MR 1798985
- Igor R. Shafarevich, Basic algebraic geometry. 2, 2nd ed., Springer-Verlag, Berlin, 1994. Schemes and complex manifolds; Translated from the 1988 Russian edition by Miles Reid. MR 1328834
- V. V. Shokurov, Prelimiting flips, Tr. Mat. Inst. Steklova 240 (2003), no. Biratsion. Geom. LineÄn. Sist. Konechno Porozhdennye Algebry, 82â219; English transl., Proc. Steklov Inst. Math. 1(240) (2003), 75â213. MR 1993750
- Carlos T. Simpson, Higgs bundles and local systems, Inst. Hautes Ătudes Sci. Publ. Math. 75 (1992), 5â95. MR 1179076, DOI 10.1007/BF02699491 Siu Y.-T. Siu. A general non-vanishing theorem and an analytic proof of the finite generation of the canonical ring. arXiv:math.AG/0610740 Taylor R. Taylor. Automorphy for some $l$-adic lifts of automorphic mod $l$ Galois representations. II. Preprint (2006).
- Michel Waldschmidt, Transcendence of periods: the state of the art, Pure Appl. Math. Q. 2 (2006), no. 2, Special Issue: In honor of John H. Coates., 435â463. MR 2251476, DOI 10.4310/PAMQ.2006.v2.n2.a3
- André Weil, Number theory, BirkhÀuser Boston, Inc., Boston, MA, 1984. An approach through history; From Hammurapi to Legendre. MR 734177, DOI 10.1007/978-0-8176-4571-7
- Claire Voisin, Théorie de Hodge et géométrie algébrique complexe, Cours Spécialisés [Specialized Courses], vol. 10, Société Mathématique de France, Paris, 2002 (French). MR 1988456, DOI 10.1017/CBO9780511615344
- E. T. Whittaker and G. N. Watson, A course of modern analysis. An introduction to the general theory of infinite processes and of analytic functions: with an account of the principal transcendental functions, Cambridge University Press, New York, 1962. Fourth edition. Reprinted. MR 0178117
- Oscar Zariski, The theorem of Riemann-Roch for high multiples of an effective divisor on an algebraic surface, Ann. of Math. (2) 76 (1962), 560â615. MR 141668, DOI 10.2307/1970376
Additional Information
- Burt Totaro
- Affiliation: Department of Pure Mathematics and Mathematical Statistics, Wilberforce Road, Cambridge CB3 0WB, England
- MR Author ID: 272212
- Email: b.totaro@dpmms.cam.ac.uk
- Received by editor(s): April 26, 2007
- Published electronically: June 22, 2007
- © Copyright 2007 Burt Totaro
- Journal: Bull. Amer. Math. Soc. 44 (2007), 541-559
- MSC (2000): Primary 14C30; Secondary 14D05, 14E05
- DOI: https://doi.org/10.1090/S0273-0979-07-01178-0
- MathSciNet review: 2338364