Algebraic geometry i complex projective varieties classics in mathematics reprint of the 1st ed berlin heidelberg new york 1976 corr 2nd printing 1981 mumford was awarded the fields medal in 1974 for his work on moduli spaces and algebraic surfaces he is presently working on the mathematics of pattern recognition and artificial . Without any doubt this is one of the very best books on algebraic surfaces now as before werner kleinert zentralblatt math vol 965 2001 the main aim of this book is to present a completely algebraic approach to the enriques classification of smooth projective surfaces defined over an algebraically closed field of arbitrary . Springer began publishing books in higher mathematics in 1920 when the series grundlehren der mathematischen wissenschaften initially conceived as a series of advanced textbooks was founded by richard courant a few years . However for both directions a solid base was still missing and the new framework of abstract algebra was just at its beginning of being applied to algebraic geometry the authors book was then a milestone in the history of the theory of algebraic surfaces and even so in algebraic geometry as a whole
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