Can someone recommend some books on commutative algebra stressing links with algebraic geometry? My concern is this. It seems to me that most of commutative algebra was formulated at least initially by algebraists, and only later were the links with geometry made more explicit. As a result, definitions which are natural to algebraists, might correspond to some complicated definitions in geometry and vice versa.
Ultimately, I would prefer a book on commutative algebra which is:
1) always reinterpreting algebraic definitions geometrically (so in some sense, written for geometers)
2) containing a lot of examples, which can be used as counterexamples to various claims, and thus exposing, rather than hiding, the subtleties of the various dictionaries between algebra and geometry
3) preferably not too big (so that it could be read entirely in a reasonable amount of time).
I have read most of Atiyah-Macdonald, and own a copy of Eisenbud's "Commutative Algebra with a view toward Algebraic Geometry". I love both books, but would like to know whether some other excellent books exist, particularly with a strong geometric bias.