A Scrapbook of Complex Curve Theory

A Scrapbook of Complex Curve Theory

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This fine book by Herb Clemens quickly became a favorite of many algebraic geometers when it was first published in 1980. It has been popular with novices and experts ever since. It is written as a book of ``impressions'' of a journey through the theory of complex algebraic curves. Many topics of compelling beauty occur along the way. A cursory glance at the subjects visited reveals a wonderfully eclectic selection, from conics and cubics to theta functions, Jacobians, and questions of moduli. By the end of the book, the theme of theta functions becomes clear, culminating in the Schottky problem. The author's intent was to motivate further study and to stimulate mathematical activity. The attentive reader will learn much about complex algebraic curves and the tools used to study them. The book can be especially useful to anyone preparing a course on the topic of complex curves or anyone interested in supplementing his/her reading.In any case, if our original equation (2.9) has coefficients in Q (or R), so does the final equation (2.13) and there is a nice bijection between (2.9) and (2.13) given in each direction by rational functions with rational coefficients. Thus we can find anbsp;...

Title:A Scrapbook of Complex Curve Theory
Author:Charles Herbert Clemens
Publisher:American Mathematical Soc. - 2002-12-10


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