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Selected Works of Phillip A. Griffiths with Commentary
Edited by: Enrico Arbarello, Università "La Sapienza", Rome, Italy, Robert L. Bryant, Duke University, Durham, NC, C. Herbert Clemens, University of Utah, Salt Lake City, UT, Maurizio Cornalba, Università di Pavia, Italy, Mark L. Green, University of California, Los Angeles, CA, Joe Harris, Harvard University, Cambridge, MA, David R. Morrison, Duke University, Durham, NC, and Wilfried Schmid, Harvard University, Cambridge, MA
A co-publication of the AMS and International Press.
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Collected Works
2003; 2598 pp; hardcover
Volume: 18
ISBN-10: 0-8218-1066-9
ISBN-13: 978-0-8218-1066-8
List Price: US$335
Member Price: US$268
Order Code: CWORKS/18
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Over the last four decades, Phillip Griffiths has been a central figure in mathematics. During this time, he made crucial contributions in several fields, including complex analysis, algebraic geometry, and differential systems. His books and papers are distinguished by a remarkably lucid style that invites the reader to understand not only the subject at hand, but also the connections among seemingly unrelated areas of mathematics. Even today, many of Griffiths' papers are used as a standard source on a subject. Another important feature of Griffiths' writings is that they often bring together classical and modern mathematics.

The four parts of Selected Works--Analytic Geometry, Algebraic Geometry, Variations of Hodge Structures, and Differential Systems--are organized according to the subject matter and are supplemented by Griffiths' brief, but extremely illuminating, personal reflections on the mathematical content and the times in which they were produced.

Griffiths' Selected Works provide the reader with a panoramic view of important and exciting mathematics during the second half of the 20th century.

This book is jointly published by the AMS and the International Press.

Readership

Graduate students and research mathematicians interested in algebraic and differential geometry.

Table of Contents

Part I. Analytic Geometry
  • P. Griffiths -- Commentary on Vector bundles
Vector Bundles
  • Ph. A. Griffiths -- The extension problem for compact submanifolds of complex manifolds I
  • P. A. Griffiths -- The extension problem in complex analysis II; embeddings with positive normal bundle
  • P. A. Griffiths -- Hermitian differential geometry, Chern classes, and positive vector bundles
  • P. A. Griffiths -- Period spaces and Hodge theory
  • P. A. Griffiths and W. Schmid -- Locally homogeneous complex manifolds
  • P. Griffiths and W. Schmid -- Recent developments in Hodge theory: A discussion of techniques and results
  • P. R. Deligne, P. Griffiths, J. Morgan, and D. Sullivan -- Real homotopy theory of Kähler manifolds
Analytic geometry
  • P. A. Griffiths -- Holomorphic mapping into canonical algebraic varieties
  • J. Carlson and P. Griffiths -- A defect relation for equidimensional holomorphic mappings between algebraic varieties
  • P. Griffiths -- Complex differentiable and integral geometry and curvature integrals associated to singularities of complex analytic varieties
  • M. Cornalba and P. Griffiths -- Analytic cycles and vector bundles on non-compact algebraic varieties
  • M. Green and P. Griffiths -- Two applications of algebraic geometry to entire holomorphic mappings
  • Acknowledgments
  • Selected titles
Part 2. Algebric Geometry
  • P. A. Griffiths -- Introductory Comments to Part 2
Cycles and deformation theory
  • P. A. Griffiths -- Some results on algebraic cycles on algebraic manifolds
  • P. A. Griffiths -- Complex-analytic properties of certain Zariski open sets on algebraic varieties
  • C. H. Clemens and P. A. Griffiths -- The intermediate Jacobian of the cubic threefold
Abel's theorem
  • P. A. Griffiths -- Variations on a theorem of Abel
  • P. Griffiths and J. Harris -- A Poncelet theorem in space
  • P. Griffiths and J. Harris -- Residues and zero-cycles on algebraic varieties
  • S. S. Chern and P. Griffiths -- Abel's theorem and webs
Algebraic and differential geometry
  • P. A. Griffiths -- Complex analysis and algebraic geometry
  • P. Griffiths and J. Harris -- Algebraic geometry and local differential geometry
Loci of divisors
  • P. Griffiths and J. Harris -- The variety of special linear systems on a general algebraic curve
  • P. Griffiths and J. Harris -- On the Noether-Lefschetz theorem and some remarks on codimension-two cycles
  • E. Arbarello, M. Cornalba, P. Griffiths, and J. Harris -- Special divisors on algebraic curves
  • Acknowledgments
  • Selected Titles
Part 3. Variations of Hodge Structures
  • P. A. Griffiths -- Introductory Comments to Part 3
Periods of integrals
  • P. A. Griffiths -- Periods of integrals on algebraic naifolds, I (Construction and properties of the modular varieties)
  • P. A. Griffiths -- Periods of integrals on algebraic manifolds, II (Local study of the period mapping)
  • Ph. A. Griffiths -- Periods of integrals on algebraic manifolds III (some global differential-geometric properties of the period mapping)
  • P. A. Griffiths -- On the periods of certain rational integrals I
  • P. A. Griffiths -- On the periods of certain rational integrals: II
  • P. A. Griffiths -- Periods of integrals on algebraic manifolds: Summary of main results and discussion of open problems
Variations of Hodge structures
  • J. Carlson, M. Green, P. Griffiths, and J. Harris -- Infinitesimal variations of Hodge structure (I)
  • P. Griffiths and J. Harris -- Infinitesimal variations of Hodge structure (II): An infinitesimal invariant of Hodge classes
  • P. A. Griffiths -- Infinitesimal variations of Hodge structure (III): Determinantal varieties and the infinitesimal invariant of normal functions
  • Acknowledgments
  • Selected Titles
Part 4. Differential Systems
  • P. A. Griffiths -- Introductory Comments to Part 4
Moving frames and differential geometry
  • P. Griffiths -- On Cartan's method of Lie groups and moving frames as applied to uniqueness and existence questions in differential geometry
Differential systems and Hodge structure
  • P. A. Griffiths -- Poincaré and algebraic geometry
  • R. L. Bryant and P. A. Griffiths -- Some observations on the infinitesimal period relations for regular threefolds with trivial canonical bundle
  • R. L. Bryant and P. Griffiths -- Reduction for constrained variational problems and \(\int\frac{1}{2} \kappa^2 ds\)
Integrability
  • P. A. Griffiths -- Linearizing flows and a cohomological interpretation of Lax equations
The characteristic variety and its geometry
  • P. A. Griffiths -- Some aspects of exterior differential systems
  • R. L. Bryant and P. A. Griffiths -- Characteristic cohomology of differential systems (I): General theory
  • R. L. Bryant and P. A. Griffiths -- Characteristic cohomology of differential systems II: conservation laws for a class of parabolic equations
  • R. Bryant, P. Griffiths, and L. Hsu -- Hyperbolic exterior differential systems and their conservation laws, Part I
  • R. Bryant, P. Griffiths, and L. Hsu -- Hyperbolic exterior differential systems and their conservation laws, Part II
  • Acknowledgments
  • Selected Titles
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