The objective of this book is to look at certain commutative graded algebras that appear
frequently in algebraic geometry. By studying classical constructions from geometry from the
point of view of modern commutative algebra this carefully-written book is a valuable source
of information offering a careful algebraic systematization and treatment of the problems at
hand and contributing to the study of the original geometric questions. In greater detail the
material covers aspects of rational maps (graph degree birationality specialization
combinatorics) Cremona transformations polar maps Gauss maps the geometry of Fitting ideals
tangent varieties joins and secants Aluffi algebras. The book includes sections of exercises
to help put in practice the theoretic material instead of the mere complementary additions to
the theory.
