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. |
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An excellent textbook for the more mature student (graduate+). It's very short yet contains all the important information in modern algebraic geometry. From the basic definition of algebraic varieties (as the name suggests) through cohomologies of sheaves and some of their applications (Riemann-Roch theorem etc.).
The material is presented very clearly, yet requires a serious effort from the reader in order to understand it fully.
One point - if you need to actually solve problems or work with algebraic geometry it's a good idea to have on hand a more detailed reference (e.g. Hartshorne) to fill in gaps where you need them.
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
abelian affine variety algebraic assume basis called Claim Clearly closed subset coherent sheaf cohomology commutative complete component Consider constant construction contained Corollary correspondence curve define definition dense determined differential dimension direct divisor element equivalence exact sequence Exercise exists extension fact field finite flabby follows genus(D geometry given gives Hence homogeneous homomorphism ideal identity induction integral invertible sheaf irreducible isomorphism k-algebra Lemma Let f limit locally free mapping module morphism multiplication natural neighborhood noetherian non-zero open covering open subset Ox-module polynomial presheaf principal problem projective Proof Proposition prove quasi-coherent rank regular function restriction result ring section of F separated sheaf sheaves smooth space with functions Spec stalk statement structure subvariety surjective Theorem theory topological space trivial true union unique vanishes zero
References to this book
Bibliographic information
| Title | Algebraic Varieties Volume 172 of Lecture note series / London mathematical society, ISSN 0076-0552 Volume 172 of London Mathematical Society Lecture Note Series, London Mathematical Society, ISSN 0076-0552 Volume 172 of London Mathematical Society Volume 172 of London Mathematical Society: London Mathematical Society lecture note series |
| Author | G. Kempf |
| Contributors | J. W. S. Cassels, N. J. Hitchin |
| Edition | illustrated, reprint |
| Publisher | Cambridge University Press, 1993 |
| ISBN | 0521426138, 9780521426138 |
| Length | 163 pages |
| Subjects | › › Mathematics / Geometry / Algebraic Mathematics / Geometry / Analytic Mathematics / Geometry / General Mathematics / Topology |
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