Post #20

«This book is intended to give a serious and reasonably complete introduction to algebraic geometry, not just for (future) experts in the field (…) For a number of reasons, algebraic geometry has earned a reputation of being inaccessible The power of the subject comes from rather abstract heavy machinery, and it is easy to lose sight of the intuitive nature of the objects and methods. (…) But there is another more optimistic perspective to be taken The ideas that allow algebraic geometry to connect several parts of mathematics are fundamental, and well-motivated Many people in nearby fields would find it useful to develop a working knowledge of the foundations of the subject, and not just at a superficial level (…) The rough edges of scheme theory have been sanded down over the past half century, although there remains an inescapable need to understand the subject on its own terms» «…in an ideal world, people would learn this material over many years, after having background courses in commutative algebra, algebraic topology, differential geometry, complex analysis, homological algebra, number theory, and French literature We do not live in an ideal world For this reason, the book is written as a first introduction, but a challenging one» https://math.stanford.edu/~vakil/216blog/FOAGsep0824public.pdf