Algebraic VarietiesIn this book, Professor Kempf gives an introduction to the theory of algebraic varieties from a sheaf theoretic standpoint. By taking this view he is able to give a clean and lucid account of the subject, which will be easily accessible to all newcomers to algebraic varieties. |
Contents
III | 1 |
V | 2 |
VI | 4 |
VII | 5 |
VIII | 8 |
IX | 10 |
X | 11 |
XI | 13 |
XLIII | 82 |
XLIV | 83 |
XLV | 85 |
XLVI | 87 |
XLVII | 88 |
XLVIII | 90 |
XLIX | 92 |
L | 94 |
XII | 15 |
XIII | 16 |
XIV | 18 |
XV | 20 |
XVI | 21 |
XVII | 25 |
XVIII | 27 |
XIX | 28 |
XX | 30 |
XXI | 31 |
XXII | 32 |
XXIII | 33 |
XXIV | 34 |
XXV | 35 |
XXVI | 36 |
XXVII | 38 |
XXIX | 42 |
XXX | 46 |
XXXI | 50 |
XXXII | 54 |
XXXIII | 56 |
XXXIV | 58 |
XXXV | 61 |
XXXVI | 62 |
XXXVII | 65 |
XXXVIII | 68 |
XXXIX | 70 |
XL | 72 |
XLI | 75 |
XLII | 80 |
Common terms and phrases
A-module abelian sheaves affine morphism affine variety algebraic group An+1 assume Claim Clearly closed subset closed subvariety coherent sheaf cohomology commutative component Consider construction Corollary define degree differential dimension dimensional direct limits direct system Exercise F₁ F₂ finite morphism finite number finite type flabby fractional ideals genus(C graph(f Hı(C Hence Hi(X homogeneous homomorphism i-homology induction injective invertible sheaf irreducible closed k-algebra k[X]-module Lemma Let f locally free mapping module morphism f natural isomorphism neighborhood nilpotents noetherian non-empty non-zero Oc,c Oc(D open affine open covering open dense subset open subset phism polynomial presheaf projective variety Proof Proposition prove quasi-coherent sheaves rank Rat(F regular function restriction Rif.F ring section of F smooth complete curve smooth curve space with functions Spec stalk subsheaf subspace surjective Theorem theory topological space trivial unique vanishes vector X₁ zero zeroes(I