## The Selected Works of Phillip A. Griffiths with Commentary: Algebraic geometryOver 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. |

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### Contents

Introductory Comments to Part 1 | 3 |

Introductiory Comments to Part 4 | 4 |

Vector Bundles | 13 |

Complexanalytic properties of certain Zariski open sets on algebraic vari | 94 |

Periods of Integrals 11 | 110 |

The Characteristic Variety and Its Geometry | 181 |

Gen | 207 |

Variations on a Theorem of Abel Invent Math 35 1976 321390 223 | 353 |

with J Harris A Poncelet theorem in space Comment Math Helvetici | 779 |

The extension problem for compact submanifolds of complex manifolds I | 781 |

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2nd fundamental form Abel's theorem Alb(S algebraic curve algebraic cycles algebraic geometry algebraic variety analytic argument assume canonical curve Chern class choose codimension cohomology complete intersection complex manifold components computation contains coordinates corresponding cubic hypersurface cubic threefold curvature Darboux frames defined definition degenerate denote differential dimension double point dual embedding equivalent fibre finite follows formula frame functions Gauss mapping given gives global Griffiths Hodge holomorphic mapping hyperplane hypersurface infinitesimal integral intermediate Jacobian irreducible isomorphism Lefschetz Lemma line bundle linearly locus Math matrix maximal rank meromorphic metric moduli non-degenerate non-singular notation open set osculating parameter plane Poincare polarized abelian variety polynomial principally polarized abelian projective space Proof properties prove quadric rational normal curve relation residue operator residue theorem result satisfying Schubert cycles sequence singular smooth span submanifold subspace subvariety Suppose tangent space universal covering vector bundle Zariski open zero