Book Review
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Book Information:
Author:
János Kollár
Title:
Shafarevich maps and automorphic forms
Additional book information:
Princeton Univ. Press, Princeton, NJ,
1995,
199 pp.,
ISBN 0-691-04381-7,
$37.50$
Aldo Andreotti and Edoardo Vesentini, Carleman estimates for the Laplace-Beltrami equation on complex manifolds, Inst. Hautes Études Sci. Publ. Math. 25 (1965), 81–130. MR 175148
M. F. Atiyah, Elliptic operators, discrete groups and von Neumann algebras, Colloque “Analyse et Topologie” en l’Honneur de Henri Cartan (Orsay, 1974) Astérisque, No. 32-33, Soc. Math. France, Paris, 1976, pp. 43–72. MR 0420729
Frédéric Campana, Remarques sur le revêtement universel des variétés kählériennes compactes, Bull. Soc. Math. France 122 (1994), no. 2, 255–284 (French, with English and French summaries). MR 1273904
Phillip Griffiths and Joseph Harris, Principles of algebraic geometry, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York, 1978. MR 507725
T. Venkatarayudu, The $7$-$15$ problem, Proc. Indian Acad. Sci., Sect. A. 9 (1939), 531. MR 0000001, DOI 10.1090/gsm/058
M. Gromov, Kähler hyperbolicity and $L_2$-Hodge theory, J. Differential Geom. 33 (1991), no. 1, 263–292. MR 1085144
Rajendra Vasant Gurjar, Coverings of algebraic varieties, Algebraic geometry, Sendai, 1985, Adv. Stud. Pure Math., vol. 10, North-Holland, Amsterdam, 1987, pp. 179–183. MR 946239, DOI 10.2969/aspm/01010179
T. Venkatarayudu, The $7$-$15$ problem, Proc. Indian Acad. Sci., Sect. A. 9 (1939), 531. MR 0000001, DOI 10.1090/gsm/058
[KR] L. Katzarkov, M. Ramachandran, On the Shafarevich conjecture for surfaces, in preparation.
János Kollár, Shafarevich maps and plurigenera of algebraic varieties, Invent. Math. 113 (1993), no. 1, 177–215. MR 1223229, DOI 10.1007/BF01244307
Terrence Napier, Convexity properties of coverings of smooth projective varieties, Math. Ann. 286 (1990), no. 1-3, 433–479. MR 1032941, DOI 10.1007/BF01453583
C. L. Siegel, Topics in complex function theory. Vol. II, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. Automorphic functions and abelian integrals; Translated from the German by A. Shenitzer and M. Tretkoff; With a preface by Wilhelm Magnus; Reprint of the 1971 edition; A Wiley-Interscience Publication. MR 1008931
I. R. Shafarevich, Basic algebraic geometry, Springer Study Edition, Springer-Verlag, Berlin-New York, 1977. Translated from the Russian by K. A. Hirsch; Revised printing of Grundlehren der mathematischen Wissenschaften, Vol. 213, 1974. MR 0447223
- [AV]
- A. Andreotti, E. Vesentini, Carleman estimates for the Laplace-Beltrami equation on complex manifolds, Publ. IHES 25 (1965) 81-130. MR 0175148
- [A]
- M. Atiyah, Elliptic operators, discrete groups and Von Neumann algebras, Astérisque 32-33 (1976), 43-72. MR 0420729
- [C]
- F. Campana, Remarque sur le revêtement universal des varieties kälheriennes compactes, Bull. Soc. Math. France 122 (1994), 255-284. MR 1273904
- [GH]
- P. Griffiths, J. Harris, Principles of Algebraic Geometry, Wiley-Interscience (1978). MR 0507725
- [GPR]
- H. Grauert, T. Peternell, R. Remmert, Several Complex Variables VII, Encyclop. Math. 74, Springer-Verlag (1994). MR 1:326 617
- [G]
- M. Gromov, Kähler hyperbolicity and Hodge theory, J. Diff. Geom. 33 (1991), 263-294. MR 1085144
- [Gu]
- R. V. Gurjar, Coverings of algebraic varieties, Adv. Stud. Pure Math. 10, 179-184, Kinokunyiya-North Holland (1987). MR 0946239
- [H]
- F. Hirzebruch, Topological Methods in Algebraic Geometry, Springer-Verlag (1978). MR 1:335 917
- [KR]
- L. Katzarkov, M. Ramachandran, On the Shafarevich conjecture for surfaces, in preparation.
- [K]
- J. Kollár, Shafarevich maps and plurigenera of algebraic varieties, Inv. Math. 113 (1993), 177-215. MR 1223229
- [N]
- T. Napier, Convexity properties of coverings of smooth projective varieties, Math. Ann. 286 (1990), 433-479. MR 1032941
- [S]
- C. L. Siegel, Topics in complex function theory, vol. 2, Wiley-Interscience (1971). MR 1008931
- [Sh]
- I. Shafarevich, Basic Algebraic Geometry, Springer-Verlag (1977). MR 0447223
Review Information:
Reviewer:
Donu Arapura
Affiliation:
Purdue University
Email:
arapura@math.purdue.edu
Journal:
Bull. Amer. Math. Soc.
33 (1996), 283-286
DOI:
https://doi.org/10.1090/S0273-0979-96-00650-7
Review copyright:
© Copyright 1996
American Mathematical Society