Topological Methods in Algebraic Geometry: Reprint of the 1978 EditionSpringer Science & Business Media, 15 févr. 1995 - 234 pages In recent years new topological methods, especially the theory of sheaves founded by J. LERAY, have been applied successfully to algebraic geometry and to the theory of functions of several complex variables. H. CARTAN and J. -P. SERRE have shown how fundamental theorems on holomorphically complete manifolds (STEIN manifolds) can be for mulated in terms of sheaf theory. These theorems imply many facts of function theory because the domains of holomorphy are holomorphically complete. They can also be applied to algebraic geometry because the complement of a hyperplane section of an algebraic manifold is holo morphically complete. J. -P. SERRE has obtained important results on algebraic manifolds by these and other methods. Recently many of his results have been proved for algebraic varieties defined over a field of arbitrary characteristic. K. KODAIRA and D. C. SPENCER have also applied sheaf theory to algebraic geometry with great success. Their methods differ from those of SERRE in that they use techniques from differential geometry (harmonic integrals etc. ) but do not make any use of the theory of STEIN manifolds. M. F. ATIYAH and W. V. D. HODGE have dealt successfully with problems on integrals of the second kind on algebraic manifolds with the help of sheaf theory. I was able to work together with K. KODAIRA and D. C. SPENCER during a stay at the Institute for Advanced Study at Princeton from 1952 to 1954. |
Table des matières
IV | 9 |
V | 16 |
VI | 37 |
VII | 49 |
VIII | 76 |
IX | 78 |
X | 81 |
XI | 84 |
XIX | 128 |
XX | 132 |
XXI | 138 |
XXII | 142 |
XXIII | 147 |
XXIV | 155 |
XXV | 159 |
XXVII | 166 |
XII | 86 |
XIII | 91 |
XIV | 94 |
XV | 96 |
XVI | 100 |
XVII | 107 |
XVIII | 114 |
XXVIII | 176 |
XXIX | 184 |
XXX | 196 |
XXXI | 202 |
XXXII | 218 |
227 | |
Expressions et termes fréquents
A₁ algebraic manifold analytic line bundles analytic sheaves analytic vector analytic vector bundle arithmetic genus associated ATIYAH b₁ BOREL C)-bundle c₁ c₂ CHERN classes cobordism coefficients cohomology class cohomology groups compact complex manifold complex analytic line complex analytic vector complex manifold complex vector bundles corresponding defined definition denoted differentiable manifold differential operator dimension element elliptic embedding equation exact sequence F₁ fibre bundle follows formula generalisation GL(q GROTHENDIECK H¹(X HIRZEBRUCH homomorphism h implies index theorem integer isomorphism KÄHLER manifold KODAIRA Lemma LIE group line bundle m-sequence Math morphism open covering open neighbourhood open set oriented differentiable manifold oriented manifolds P₁ P₂ paracompact space polynomial PONTRJAGIN classes power series presheaf principal bundle prove RIEMANN-ROCH theorem ring SERRE sheaf of germs spectral sequence structure group subgroup submanifold tangent bundle TODD genus topological space trivial V₁ vector bundle vector space virtual zero
Fréquemment cités
Page 222 - KODAIRA, K. : [!] The theorem of RIEMANN-ROCH on compact analytic surfaces.