tailieunhanh - ALGEBRAIC CURVES - An Introduction to Algebraic Geometry

The second thing that is notable in the programs of the high achieving countries is the level of abstraction that is present in the problems students are expected to do in these early grades. Variables have been introduced and are routinely used, so students set up and solve simple equations in second grade and quite sophisticated equations in third grade. There is a strong belief in the education community in the United States that “young students learn strictly in context,” which means that they do not believe young students can handle abstraction. This belief is not supported by research, nor is it supported by the outcomes in the. | ALGEBRAIC CURVES An Introduction to Algebraic Geometry WILLIAM FULTON January 28 2008 Preface Third Preface 2008 This text has been out of print for several years with the author holding copyrights. Since I continue to hear from young algebraic geometers who used this as their first text I am glad now to make this edition available without charge to anyone interested. I am most grateful to Kwankyu Lee for making a careful LaTeX version which was the basis of this edition thanks also to Eugene Eisenstein for help with the graphics. As in 1989 I have managed to resist making sweeping changes. I thank all who have sent corrections to earlier versions especially Grzegorz Bobinski for the most recent and thorough list. It is inevitable that this conversion has introduced some new errors and I and future readers will be grateful if you will send any errors you find to me at wfulton@. Second Preface 1989 When this book first appeared there were few texts available to a novice in modern algebraic geometry. Since then many introductory treatises have appeared including excellent texts by Shafarevich Mumford Hartshorne Griffiths-Harris Kunz Clemens Iitaka Brieskorn-Knorrer and Arbarello-Cornalba-Griffiths-Harris. The past two decades have also seen a good deal of growth in our understanding of the topics covered in this text linear series on curves intersection theory and the Riemann-Roch problem. It has been tempting to rewrite the book to reflect this progress but it does not seem possible to do so without abandoning its elementary character and destroying its original purpose to introduce students with a little algebra background to a few of the ideas of algebraic geometry and to help them gain some appreciation both for algebraic geometry and for origins and applications of many of the notions of commutative algebra. If working through the book and its exercises helps prepare a reader for any of the texts mentioned above that will be an added benefit.