Book Review
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MathSciNet review:
3307764
Full text of review:
PDF
This review is available free of charge.
Book Information:
Author:
Igor V. Dolgachev
Title:
Classical algebraic geometry: A modern view
Additional book information:
Cambridge University Press,
Cambridge,
2012,
xii+639 pp.,
ISBN 978-1-107-01765-8,
hardcover
Daniel Allcock, James A. Carlson, and Domingo Toledo, A complex hyperbolic structure for moduli of cubic surfaces, C. R. Acad. Sci. Paris Sér. I Math. 326 (1998), no. 1, 49–54 (English, with English and French summaries). MR 1649469, DOI 10.1016/S0764-4442(97)82711-5
Daniel Allcock, James A. Carlson, and Domingo Toledo, The complex hyperbolic geometry of the moduli space of cubic surfaces, J. Algebraic Geom. 11 (2002), no. 4, 659–724. MR 1910264, DOI 10.1090/S1056-3911-02-00314-4
Mauro C. Beltrametti, Ettore Carletti, Dionisio Gallarati, and Giacomo Monti Bragadin, Lectures on curves, surfaces and projective varieties, EMS Textbooks in Mathematics, European Mathematical Society (EMS), Zürich, 2009. A classical view of algebraic geometry; Translated from the 2003 Italian original by Francis Sullivan. MR 2549804, DOI 10.4171/064
Fedor Bogomolov and Yuri Prokhorov, On stable conjugacy of finite subgroups of the plane Cremona group, I, Cent. Eur. J. Math. 11 (2013), no. 12, 2099–2105. MR 3111709, DOI 10.2478/s11533-013-0314-9
A. Cayley, On the triple tangent planes of surfaces of the third order, Cambridge and Dublin Math. J., 4 (1849), 118–138.
L. Cremona, Sulla trasformazioni geometriche delle figure piane, Giornale di matematiche di Battaglini 1 (1863), 305–311.
Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157
V. A. Iskovskih, Anticanonical models of three-dimensional algebraic varieties, Current problems in mathematics, Vol. 12 (Russian), VINITI, Moscow, 1979, pp. 59–157, 239 (loose errata) (Russian). MR 537685
J. Lüroth, Einige Eigenschaften einer gewissen Gattung von Curven vierter Ordnung, Math. Ann. 1 (1869), no. 1, 37–53 (German). MR 1509610, DOI 10.1007/BF01447385
Shigefumi Mori and Shigeru Mukai, Classification of Fano $3$-folds with $B_{2}\geq 2$, Manuscripta Math. 36 (1981/82), no. 2, 147–162. MR 641971, DOI 10.1007/BF01170131
J. Plücker, Theorie der algebraischen Kurven: Gegründet auf eine neue Behandlungsweise der analytischen Geometrie. Adolph Marcus, Berlin, 1839.
J. Sylvester, Sketch of a memoir on elimination, transformation, and canonical forms, Cambridge and Dublin Math. J., 6 (1851), 186-200.
References
- Daniel Allcock, James A. Carlson, and Domingo Toledo, A complex hyperbolic structure for moduli of cubic surfaces, C. R. Acad. Sci. Paris Sér. I Math. 326 (1998), no. 1, 49–54 (English, with English and French summaries). MR 1649469 (2001h:14042), DOI 10.1016/S0764-4442(97)82711-5
- Daniel Allcock, James A. Carlson, and Domingo Toledo, The complex hyperbolic geometry of the moduli space of cubic surfaces, J. Algebraic Geom. 11 (2002), no. 4, 659–724. MR 1910264 (2003m:32011), DOI 10.1090/S1056-3911-02-00314-4
- Mauro C. Beltrametti, Ettore Carletti, Dionisio Gallarati, and Giacomo Monti Bragadin, Lectures on curves, surfaces and projective varieties, A classical view of algebraic geometry, EMS Textbooks in Mathematics, European Mathematical Society (EMS), Zürich, 2009. Translated from the 2003 Italian original by Francis Sullivan. MR 2549804 (2010k:14001), DOI 10.4171/064
- Fedor Bogomolov and Yuri Prokhorov, On stable conjugacy of finite subgroups of the plane Cremona group, I, Cent. Eur. J. Math. 11 (2013), no. 12, 2099–2105. MR 3111709, DOI 10.2478/s11533-013-0314-9
- A. Cayley, On the triple tangent planes of surfaces of the third order, Cambridge and Dublin Math. J., 4 (1849), 118–138.
- L. Cremona, Sulla trasformazioni geometriche delle figure piane, Giornale di matematiche di Battaglini 1 (1863), 305–311.
- Robin Hartshorne, Algebraic geometry. Graduate Texts in Mathematics, No. 52. Springer-Verlag, New York 1977. MR 0463157 (57 \#3116)
- V. A. Iskovskih, Anticanonical models of three-dimensional algebraic varieties, Current Problems in Mathematics, Vol. 12 (Russian), VINITI, Moscow, 1979, pp. 59–157, 239 (loose errata) (Russian). MR 537685 (81i:14026b)
- J. Lüroth, Einige Eigenschaften einer gewissen Gattung von Curven vierter Ordnung, Math. Ann. 1 (1869), no. 1, 37–53 (German). MR 1509610, DOI 10.1007/BF01447385
- Shigefumi Mori and Shigeru Mukai, Classification of Fano $3$-folds with $B_{2}\geq 2$, Manuscripta Math. 36 (1981/82), no. 2, 147–162. MR 641971 (83f:14032), DOI 10.1007/BF01170131
- J. Plücker, Theorie der algebraischen Kurven: Gegründet auf eine neue Behandlungsweise der analytischen Geometrie. Adolph Marcus, Berlin, 1839.
- J. Sylvester, Sketch of a memoir on elimination, transformation, and canonical forms, Cambridge and Dublin Math. J., 6 (1851), 186-200.
Review Information:
Reviewer:
Lev A. Borisov
Affiliation:
Rutgers University
Journal:
Bull. Amer. Math. Soc.
52 (2015), 129-134
DOI:
https://doi.org/10.1090/S0273-0979-2014-01453-3
Published electronically:
May 29, 2014
Review copyright:
© Copyright 2014
American Mathematical Society
