Math 536   Algebraic Geometry
 
Text Book: Basic Algebraic Geometry I (Varieties in Projective Spaces)
by Igor R. Shafarevich,  2nd Edition, Springer-Verlag
ISBN 3-540-54812-2

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Algebraic Geometry is one of the oldest and yet still fast developing
fields in mathematics.  In this course I will selectively cover most
of Shafarevich's Basic Algebraic Geometry I.

The back cover of the book vividly characterizes the style of the book
which coincides with my own philosophy of teaching:

"The approach of this book is aimed at the substance of algebraic geometry
rather than the formalism. The topics are well chosen, and discussed at a
level of generality and rigor that will be attractive to a wide range of
students. The motivation behind the material is thoroughly discussed and
illustrated by substantial examples."

This course is not just for someone who wants to write a thesis in
algebraic geometry, it is for everyone who may use results and
techniques of algebraic geometry one way or another. For this, let me
quote the English translator of the book, Miles Reid (who himself is a
very accomplished algebraic geometer):

"For many students, it is just not feasible both to do the research
for a Ph.D thesis and to master all the technical foundations of
algebraic geometry at the same time. In any case, even if you have
mastered everything in scheme theory, your research may well take you
into number theory or differential geometry or representation theory
or math physics, and you will have just as many new technical things
to learn there. For all such students, and for the many specialists in
other branches of math who need a liberal education in algebraic
geometry, Shafarevich's book is a must."

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The course is scheduled at 3:00 -- 4:15 WF. If you are interested in
taking this course and have a conflict with the time, please let me
know, and we will try to make adjustment.