immediate formal precision. Following this thought, the aim of the course
on which this book is based was not to give formal proofs, but rather to give
heuristic ideas and suggestive arguments. In other words, the aim was not
to make a legal presentation, but to help people learn. This should prepare
the students to read up, or better still, make up, formal proofs if and when
desired. So readability is a primary goal of this book. Preference is given
to motivation over formality. Thus, this book is not meant to prepare the
student for formal examinations, but to really learn the subject; not qualifiers,
but original investigations.
I have tried to tell the story of algebraic geometry and to bring out the
poetry in it. I shall be glad if this helps the reader to enjoy the subject while
This work was partly supported by NSF grant DMS88-16286, ONR grant
N00014-88-K-0402, and ARO contract DAAG29-85-C-0018 under Cornell
MSI at Purdue University. I am grateful for this support. My thanks are
also due to P. Keskar, W. Li, and I. Yie for help in proofreading, and to Y.
Abhyankar for everything.
Shreeram S. Abhyankar
18 January 1990