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Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

Euler and algebraic geometry

Author(s): Burt Totaro
Journal: Bull. Amer. Math. Soc. 44 (2007), 541-559.
MSC (2000): Primary 14C30; Secondary 14D05, 14E05
Posted: June 22, 2007
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References:

1.
Y. André. $ G$-functions and geometry. Vieweg (1989). MR 990016 (90k:11087)

2.
Y. André and F. Baldassarri. Geometric theory of $ G$-functions. Arithmetic geometry (Cortona, 1994), 1-22. Cambridge (1997). MR 1472489 (99c:12011)

3.
A. Beauville. Les familles stables de courbes elliptiques sur $ \mathbf{P}^1$ admettant quatre fibres singulières. C. R. Acad. Sci. Paris 294 (1982), 657-660. MR 664643 (83h:14008)

4.
B. Ben Hamed and L. Gavrilov. Families of Painlevé VI equations having a common solution. Int. Math. Res. Not. 2005, no. 60, 3727-3752. MR 2205113

5.
C. Birkar, P. Cascini, C. Hacon, and J. McKernan. Existence of minimal models for varieties of log general type. arXiv:math.AG/0610203

6.
P. Boalch. From Klein to Painlevé via Fourier, Laplace and Jimbo. Proc. London Math. Soc. 90 (2005), 167-208. MR 2107041 (2005h:34233)

7.
P. Candelas, X. de la Ossa, P. Green, and L. Parkes. A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory. Nuclear Phys. B. 359 (1991), 21-74. MR 1115626 (93b:32029)

8.
J. Carlson, S. Müller-Stach, and C. Peters. Period mappings and period domains. Cambridge (2003). MR 2012297 (2005a:32014)

9.
A. Chambert-Loir. Théorèmes d'algébricité en géométrie diophantienne (d'après J.-B. Bost, Y. André, D. & G. Chudnovsky). Séminaire Bourbaki 2000/2001, Astérisque 282 (2002), 175-209. MR 1975179 (2004f:11062)

10.
D. Chudnovsky and G. Chudnovsky. Applications of Padé approximations to the Grothendieck conjecture on linear differential equations. Number theory (New York, 1983-84), 52-100. LNM 1135, Springer (1985). MR 803350 (87d:11053)

11.
K. Corlette and C. Simpson. On the classification of rank two representations of quasiprojective fundamental groups. arXiv:math.AG/0702287

12.
A. Corti, ed. Flips for 3-folds and 4-folds. Oxford (2007).

13.
P. Deligne. Equations différentielles à points singuliers régulières. LNM 163, Springer (1970). MR 0417174 (54:5232)

14.
B. Dubrovin. Painlevé transcendents in two-dimensional topological field theory. The Painlevé property, 287-412. Springer (1999). MR 1713580 (2001h:53131)

15.
B. Dubrovin and M. Mazzocco. Monodromy of certain Painlevé-VI transcendents and reflection groups. Invent. Math. 141 (2000), 55-147. MR 1767271 (2001j:34114)

16.
B. Dwork, G. Gerotto and F. Sullivan. An introduction to $ G$-functions. Princeton (1994). MR 1274045 (96c:12009)

17.
L. Euler. Solutio generalis quorundam problematum Diophanteorum quae vulgo nonnisi solutiones speciales admittere videntur. Leonhardi Euleri opera omnia, v. 1, pt. 2, 428-458. Teubner (1915).

18.
L. Euler. Introduction to analysis of the infinite, 2 vols. Springer (1988, 1990). MR 715928 (85d:01030)

19.
J.-M. Fontaine and B. Mazur. Geometric Galois representations. Elliptic curves, modular forms, & Fermat's last theorem (Hong Kong, 1993), 41-78. International Press (1995). MR 1363495 (96h:11049)

20.
W. Goldman and W. Neumann. Homological action of the modular group on some cubic moduli spaces. Math. Res. Lett. 12 (2005), 575-591. MR 2155233 (2006h:57015)

21.
P. Griffiths. Periods of integrals on algebraic manifolds: summary of main results and discussion of open problems. Bull. AMS 75 (1970), 228-290. MR 0258824 (41:3470)

22.
M. Harris, N. Shepherd-Barron, and R. Taylor. A family of Calabi-Yau varieties and potential automorphy. Preprint (2006).

23.
N. Hitchin. Poncelet polygons and the Painlevé equations. Geometry and analysis (Bombay, 1992), 151-185. Tata Inst. Fund. Res. (1995). MR 1351506 (97d:32042)

24.
R.-P. Holzapfel. Geometry and arithmetic around Euler partial differential equations. D. Reidel (1986).MR 0867406 (88b:32075)

25.
K. Hori, S. Katz, A. Klemm, R. Pandharipande, R. Thomas, C. Vafa, R. Vakil, and E. Zaslow. Mirror symmetry. AMS (2003). MR 2003030 (2004g:14042)

26.
D. Husemöller. Elliptic curves. Springer (2004). MR 2024529 (2005a:11078)

27.
K. Iwasaki, H. Kimura, S. Shimomura, and M. Yoshida. From Gauss to Painlevé: a modern theory of special functions. Vieweg (1991). MR 1118604 (92j:33001)

28.
N. Katz. Nilpotent connections and the monodromy theorem: applications of a result of Turrittin. Publ. Math. IHES 39 (1970), 175-232. MR 0291177 (45:271)

29.
N. Katz. Algebraic solutions of differential equations ($ p$-curvature and the Hodge filtration). Invent. Math. 18 (1972), 1-118. MR 0337959 (49:2728)

30.
N. Katz. Rigid local systems. Princeton (1996). MR 1366651 (97e:14027)

31.
F. Klein and R. Fricke. Vorlesungen über die Theorie der elliptischen Modulfunktionen, v. 1. Teubner (1890).

32.
J. Kollár, K. Smith, and A. Corti. Rational and nearly rational varieties. Cambridge (2004). MR 2062787 (2005i:14063)

33.
M. Kontsevich and D. Zagier. Periods. Mathematics unlimited, 771-808. Springer (2001). MR 1852188 (2002i:11002)

34.
S. Mori. Flip theorem and the existence of minimal models for 3-folds. J. Amer. Math. Soc. 1 (1988), 117-253. MR 924704 (89a:14048)

35.
M. Reid. Twenty-five years of 3-folds - an old person's view. Explicit birational geometry of 3-folds, 313-343. Cambridge (2000). MR 1798985 (2002b:14001)

36.
I. Shafarevich. Basic algebraic geometry, 2 vols. Springer (1994). MR 1328834 (95m:14002)

37.
V. Shokurov. Prelimiting flips. Tr. Mat. Inst. Steklova 240 (2003), 82-219. MR 1993750 (2004k:14024)

38.
C. Simpson. Higgs bundles and local systems. Publ. Math. IHES 75 (1992), 5-95. MR 1179076 (94d:32027)

39.
Y.-T. Siu. A general non-vanishing theorem and an analytic proof of the finite generation of the canonical ring. arXiv:math.AG/0610740

40.
R. Taylor. Automorphy for some $ l$-adic lifts of automorphic mod $ l$ Galois representations. II. Preprint (2006).

41.
M. Waldschmidt. Transcendence of periods: the state of the art. Pure Appl. Math. Q. 2 (2006), 435-463. MR 2251476 (2007d:11083)

42.
A. Weil. Number theory: an approach through history. Birkhäuser (1984). MR 734177 (85c:01004)

43.
C. Voisin. Hodge theory and complex algebraic geometry, 2 vols. Cambridge (2002, 2003). MR 1988456 (2005c:32024a)

44.
E. Whittaker and G. Watson. A course of modern analysis. Cambridge (1962).MR 0178117 (31:2375)

45.
O. Zariski. The theorem of Riemann-Roch for high multiples of an effective divisor on an algebraic surface. Appendix by D. Mumford. Ann. Math. 76 (1962), 560-615. MR 0141668 (25:5065)


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Additional Information:

Burt Totaro
Affiliation: Department of Pure Mathematics and Mathematical Statistics, Wilberforce Road, Cambridge CB3 0WB, England
Email: b.totaro@dpmms.cam.ac.uk

DOI: 10.1090/S0273-0979-07-01178-0
PII: S 0273-0979(07)01178-0
Received by editor(s): April 26, 2007
Posted: June 22, 2007
Copyright of article: Copyright 2007, Burt Totaro


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