Author | Kendig, Keith. author |
---|---|
Title | Elementary Algebraic Geometry [electronic resource] / by Keith Kendig |
Imprint | New York, NY : Springer New York, 1977 |
Connect to | http://dx.doi.org/10.1007/978-1-4615-6899-5 |
Descript | 309 p. 40 illus. online resource |
I Examples of curves -- 1 Introduction -- 2 The topology of a few specific plane curves -- 3 Intersecting curves -- 4 Curves over ? -- II Plane curves -- 1 Projective spaces -- 2 Affine and projective varieties; examples -- 3 Implicit mapping theorems -- 4 Some local structure of plane curves -- 5 Sphere coverings -- 6 The dimension theorem for plane curves -- 7 A Jacobian criterion for nonsingularity -- 8 Curves in ?2(?) are connected -- 9 Algebraic curves are orientable -- 10 The genus formula for nonsingular curves -- III Commutative ring theory and algebraic geometry -- 1 Introduction -- 2 Some basic lattice-theoretic properties of varieties and ideals -- 3 The Hilbert basis theorem -- 4 Some basic decomposition theorems on ideals and varieties -- 5 The Nullstellensatz: Statement and consequences -- 6 Proof of the Nullstellensatz -- 7 Quotient rings and subvarieties -- 8 Isomorphic coordinate rings and varieties -- 9 Induced lattice properties of coordinate ring surjections; examples -- 10 Induced lattice properties of coordinate ring injections -- 11 Geometry of coordinate ring extensions -- IV Varieties of arbitrary dimension -- 1 Introduction -- 2 Dimension of arbitrary varieties -- 3 The dimension theorem -- 4 A Jacobian criterion for nonsingularity -- 5 Connectedness and orientability -- 6 Multiplicity -- 7 Bรฉzoutโs theorem -- V Some elementary mathematics on curves -- 1 Introduction -- 2 Valuation rings -- 3 Local rings -- 4 A ring-theoretic characterization of nonsingularity -- 5 Ideal theory on a nonsingular curve -- 6 Some elementary function theory on a nonsingular curve -- 7 The Riemann-Roch theorem -- Notation index