Naturally there were a number of seminars, and this volume is essentially the proceedings of one of these. The motif of the seminar was to explore the ways in which the recent developments in formal Hodge theory might be applied to problems in algebraic geometry. Differential systems and isometric embeddings by Phillip Griffiths Book 20 editions published between and in English and Russian and held by WorldCat member libraries worldwide The theory of exterior differential systems provides a framework for systematically addressing the typically non-linear, and frequently overdetermined, partial differential equations that arise in differential geometry.
Adaptation of the techniques of microlocalization to differential systems have led to recent activity on the foundations of the theory; in particular, the fundamental role of the characteristic variety in geometric problems is now clearly established.
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In this book the general theory is explained in a relatively quick and concrete manner, and then this general theory is applied to the recent developments in the classical problem of isometric embeddings of Riemannian manifolds. Exterior differential systems and the calculus of variations by Phillip Griffiths Book 19 editions published between and in 3 languages and held by WorldCat member libraries worldwide 15 0. Introduction to algebraic curves by Phillip Griffiths Book 29 editions published between and in English and Undetermined and held by WorldCat member libraries worldwide.
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- Slice filtration on motives and the Hodge conjecture (with an appendix by J. Ayoub).
Geometry of algebraic curves by E Arbarello 24 editions published between and in English and held by WorldCat member libraries worldwide The second volume of the Geometry of Algebraic Curves is devoted to the foundations of the theory of moduli of algebraic curves. Its authors are research mathematicians who have actively participated in the development of the Geometry of Algebraic Curves. The subject is an extremely fertile and active one, both within the mathematical community and at the interface with the theoretical physics community. The careful and comprehensive presentation of the material will be of value to students who wish to learn the subject and to experts as a reference source.
The first volume appeared as volume of the same series. Topics in algebraic and analytic geometry; notes from a course of Phillip Griffiths by Phillip Griffiths Book 23 editions published between and in English and held by WorldCat member libraries worldwide. Geometry of algebraic curves by E Arbarello Book in English and held by WorldCat member libraries worldwide In recent years there has been enormous activity in the theory of algebraic curves.
Many long-standing problems have been solved using the general techniques developed in algebraic geometry during the 's and 's. Additionally, unexpected and deep connections between algebraic curves and differential equations have been uncovered, and these in turn shed light on other classical problems in curve theory.
It seems fair to say that the theory of algebraic curves looks completely different now from how it appeared 15 years ago; in particular, our current state of knowledge repre sents a significant advance beyond the legacy left by the classical geometers such as Noether, Castelnuovo, Enriques, and Severi.
These books give a presentation of one of the central areas of this recent activity; namely, the study of linear series on both a fixed curve Volume I and on a variable curve Volume II. Our goal is to give a comprehensive and self-contained account of the extrinsic geometry of algebraic curves, which in our opinion constitutes the main geometric core of the recent advances in curve theory.
Along the way we shall, of course, discuss appli cations of the theory of linear series to a number of classical topics e. The topic of the conference was "Special divisors on algebraic curves, ". This monograph gives an exposition of the elementary aspects of the theory of special divisors together with an explanation of some more advanced results that are not too technical. As such, it is intended to be an introduction to recent sources. As with most subjects, one may approach the theory of special divisors from several points of view.
The one adopted here pertains to Clifford's theorem, and may be informally stated as follo. On the tangent space to the space of algebraic cycles on a smooth algebraic variety by M Green Book 12 editions published between and in English and held by WorldCat member libraries worldwide In recent years, considerable progress has been made in studying algebraic cycles using infinitesimal methods.
These methods have usually been applied to Hodge-theoretic constructions such as the cycle class and the Abel-Jacobi map. Substantial advances have also occurred in the infinitesimal theory for subvarieties of a given smooth variety, centered around the normal bundle and the obstructions coming from the normal bundle's first cohomology group.
Here, Mark Green and Phillip Griffiths set forth the initial stages of an infinitesimal theory for algebraic cycles. The book aims in part to understand the geometric basis and the limitations of Spencer Bloch's beautiful formula for the tangent space to Chow groups.
Bloch's formula is motivated by algebraic K-theory and involves differentials over Q. The theory developed here is characterized by the appearance of arithmetic considerations even in the local infinitesimal theory of algebraic cycles. Create Alert. Share This Paper. Citations Publications citing this paper.
Aravind Asok , Paul arne Ostvaer. Intermediate Jacobians and the slice filtration Doosung Park. Mixed Artin-Tate motives over number rings Jakob Scholbach. References Publications referenced by this paper. Triangulated categories of motives over a eld Vladimir Voevodsky. Chern Jahresber. Revue Internationale. Complex differential and integral geometry and curvature integrals associated to singularities of complex analytic varieties Phillip A. An inequality for the rank of a web and webs of maximum rank. Classe di Scienze. Serie IV. A theorem concerning the differential equations satisfied by normal functions associated to algebraic cycles.
Complex analysis and algebraic geometry Phillip A. Griffiths American Mathematical Society.
New Series. Algebraic geometry and local differential geometry Phillip A. Die Geometrie in der zeitgenossischen Mathematik Phillip A. On the variety of special linear systems on a general algebraic curve Phillip A. Infinitesimal variations of Hodge structure and the global Torelli problem Phillip A. Griffiths, James A. Neron models for general normal functions R. Donagi unpublished notes.
An observation on normal functions Phillip A. Griffiths Symposia Mathematica, Sympos. XXIV Some isometric embedding and rigidity results for Riemannian manifolds Phillip A. Griffiths, E. Berger, R. Infinitesimal variations of Hodge structure, I Phillip A. Carlson, M. Green, J. Harris Compositio Mathematica. Infinitesimal variations of Hodge structure, II. An infinitesimal invariant of Hodge classes Phillip A. Infinitesimal variations of Hodge structure. Determinantal varieties and the infinitesimal invariant of normal functions Phillip A.
The Gauss equations and rigidity of isometric embeddings Phillip A. Bryant Duke Mathematical Journal. Characteristics and existence of isometric embeddings Phillip A. Griffiths, R. Bryant, D. Yang Duke Mathematical Journal. Some observations on the infinitesimal period relations for regular threefolds with trivial canonical bundle Phillip A. Bryant Arithmetic and geometry. II Progr. Linearizing flows and a cohomology interpretation of Lax equations Phillip A.
Griffiths Seminar on nonlinear partial differential equations Berkeley, Calif. Variation of Hodge structure. Topics in transcendental algebraic geometry Princeton, N.framroraho.tk
Griffiths, Phillip [WorldCat Identities]
Griffiths, L. Tu Annals of Mathematics Studies. Press, Princeton, NJ. Curvature properties of the Hodge bundles. Infinitesimal variation of Hodge structure. Asymptotic behavior of a variation of Hodge structure. Infinitesimal variation of Hodge structure and the generic global Torelli theorem. On the Noether-Lefschetz theorem and some remarks on codimension-two cycles Phillip A. Harris Mathematische Annalen.
Bryant American Journal of Mathematics. Linearizing flows and a cohomological interpretation of Lax equations Phillip A. Chern: always changing, always the same Phillip A. Griffiths Chern—a great geometer of the twentieth century.
Characteristic cohomology of differential systems, I. General theory Phillip A. Bryant Journal of the American Mathematical Society. Characteristic cohomology of differential systems, II.