Reprinted with permission from CHOICE, © American Library Association.

*Mauro C. Beltrametti* (University of Genova, Italy)

*Ettore Carletti* (University of Genova, Italy)

*Dionisio Gallarati* (University of Genova, Italy)

*Giacomo Monti Bragadin* (University of Genova, Italy)

A Classical View of Algebraic Geometry

EMS Textbooks in Mathematics

ISBN 978-3-03719-064-7

DOI 10.4171/064

August 2009, 506 pages, hardcover, 16.5 x 23.5 cm.

58.00 Euro

Among mathematical subjects, algebraic geometry arguably stands as both
most ancient and most modern (with number theory, now its intimate ally,
the only rival on either front). But such a long, active history creates
pedagogical challenges at the undergraduate level, where the subject
currently suffers systematic neglect despite its venerable centrality.
Any approach that does not seem old-fashioned and naïve to some runs the
risk of seeming overly sophisticated, abstruse, and remote to others,
and vice versa. M. Reid's *Undergraduate Algebraic Geometry* (CH,
Dec'89, 27-2141) strikes perhaps a perfect balance, but that short,
breathless book functions as only an invitation or sampler. Here, one
has a systematic development, unique in aiming at the same audience as
Reid, but providing thorough preparation for eventual graduate-level
study out of treatises such as the ones by Phillip Griffiths and Joseph
Harris or Robin Hartshorne. Though Beltrametti and colleagues (all,
Univ. of Genova, Italy) concentrate on classical topics such as Cremona
transformations and omit modern tools such as Grothendieck's schemes,
experts will readily detect how the modern viewpoint really informs
these authors' approach, the better to smooth any future transition for
students first entering the subject.

Summing Up: Recommended. Upper-division undergraduate mathematics collections.