The Red Book of Varieties and Schemes: Includes the Michigan Lectures (1974) on Curves and their Jacobians
Mumford's famous Red Book gives a simple readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduate students or mathematicians in other fields wishing to learn quickly what algebraic geometry is all about.
This new edition also includes an overview of the theory of curves, their moduli spaces and their Jacobians, one of the most exciting fields within algebraic geometry. The book is aimed at graduate students and professors seeking to learn
i) the concept of "scheme" as part of their study of algebraic geometry and
ii) an overview of moduli problems for curves and of the use of theta functions to study these.
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abelian variety affine open affine variety algebraic geometry algebraically closed field assume bijection birational canonical closed point closed subscheme closed subset closed subvariety closure codimension commutative components coordinate ring Corollary corresponding define Definition differentials dimension elements equation étale Example fact fibre product finite morphism finite set finite type flat follows functor genus g hence homogeneous coordinates homomorphism induced injective integral domain intersection isomorphism Jacobian k-valued Lecture lemma Let f linear maximal ideal module morphism f nilpotent noetherian non-singular non-zero normal open affine sets open neighbourhood open sets open subset ox-module Pn(k polynomial prescheme prevariety prime ideal projective variety Proof Proposition prove quasi-coherent quotient field R-module restriction scheme sheaf Spec Spec(R subring subspace Suppose surjective tangent cone tangent space theorem topological space topology U C X valuation ring Zariski Zariski topology Zariski-Samuel zeroes