Topics in Algebraic and Analytic Geometry (eBook)

Notes From a Course of Phillip Griffiths

John Frank Adams, Phillip A. Griffiths (Autoren)

eBook Download: PDF

2015
228 Seiten
Princeton University Press (Verlag)
978-1-4008-6926-8 (ISBN)

Infos

This volume offers a systematic treatment of certain basic parts of algebraic geometry, presented from the analytic and algebraic points of view. The notes focus on comparison theorems between the algebraic, analytic, and continuous categories.Contents include: 1.1 sheaf theory, ringed spaces; 1.2 local structure of analytic and algebraic sets; 1.3 Pn 2.1 sheaves of modules; 2.2 vector bundles; 2.3 sheaf cohomology and computations on Pn; 3.1 maximum principle and Schwarz lemma on analytic spaces; 3.2 Siegel's theorem; 3.3 Chow's theorem; 4.1 GAGA; 5.1 line bundles, divisors, and maps to Pn; 5.2 Grassmanians and vector bundles; 5.3 Chern classes and curvature; 5.4 analytic cocycles; 6.1 K-theory and Bott periodicity; 6.2 K-theory as a generalized cohomology theory; 7.1 the Chern character and obstruction theory; 7.2 the Atiyah-Hirzebruch spectral sequence; 7.3 K-theory on algebraic varieties; 8.1 Stein manifold theory; 8.2 holomorphic vector bundles on polydisks; 9.1 concluding remarks; bibliography.Originally published in 1974.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Produkt-Details

• Erscheint lt. Verlag: 8.3.2015
• Reihe/Serie: Mathematical Notes
• Reihe/Serie: Mathematical Notes
• Reihe/Serie: Monographs in Population Biology
• Reihe/Serie: Princeton Legacy Library
• Reihe/Serie: Princeton Legacy Library
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: Additive map • affine variety • Algebraic Curve • Algebraic Geometry • Algebraic operation • algebraic surface • algebraic variety • analytic continuation • Analytic set • Analytic space • Atiyah–Hirzebruch spectral sequence • automorphism • Bott periodicity theorem • Cauchy's Integral Formula • Chern class • Chow's theorem • Codimension • Coherence condition • cohomology • Cohomology operation • Cohomology ring • Cokernel • Commutative diagram • comparison theorem • complex manifold • Complex vector bundle • de Rham cohomology • Diagram (category theory) • differentiable manifold • differential form • Differential Geometry • Differential topology • Dimension (vector space) • Divisor • Divisor (algebraic geometry) • Duality (mathematics) • Epimorphism • Equation • exact sequence • fiber bundle • Fundamental class • general linear group • Grassmannian • Group homomorphism • Hilbert's syzygy theorem • holomorphic function • Holomorphic sheaf • Holomorphic vector bundle • Homomorphism • Homotopy • Homotopy group • Irreducibility (mathematics) • isomorphism class • Jacobian matrix and determinant • K-theory • Laurent Series • Lie derivative • Linear map • line bundle • manifold • Mathematical Induction • Measure (mathematics) • Meromorphic Function • Module (mathematics) • Morphism • Neighbourhood (mathematics) • Obstruction theory • polynomial • power series • Presheaf (category theory) • principal bundle • Product topology • projective space • projective variety • Resolution of Singularities • Riemann surface • ring homomorphism • Ring (mathematics) • Schwarz lemma • sheaf cohomology • Sheaf (mathematics) • sheaf of modules • simplicial complex • Special case • Spectral Sequence • Stein manifold • submanifold • Subset • Surjective function • tangent bundle • Tangent Space • Tensor Algebra • Theorem • Topological space • Topology • transcendence degree • Variable (mathematics) • vector bundle • Weierstrass preparation theorem • Zariski topology
• ISBN-10: 1-4008-6926-9 / 1400869269
• ISBN-13: 978-1-4008-6926-8 / 9781400869268