New Trends in Algebraic Geometry (London Mathematical Society Lecture Note Series, Series Number 264)

This book is the outcome of the 1996 Warwick Algebraic Geometry EuroConference, containing seventeen survey and research articles selected from the most outstanding contemporary research topics in algebraic geometry. Several of the articles are expository: among these a beautiful short exposition by Paranjape of the new and very simple approach to the resolution of singularities; a detailed essay by Ito and Nakamura on the ubiquitous A,D,E classification, centered around simple surface singularities; a discussion by Morrison of the new special Lagrangian approach to giving geometric foundations to mirror symmetry; and two deep, informative surveys by Siebert and Behrend on Gromow-Witten invariants, treating them from the point of view of algebraic and symplectic geometry. The remaining articles cover a wide cross section of the most significant research topics in algebraic geometry. This includes Gromow-Witten invariants, Hodge theory, Calabi-Yau 3-folds, mirror symmetry and classification of varieties. Cover......Page 1 Frontmatter......Page 2 Contents......Page 6 Foreword......Page 8 Birational Calabi--Yau n-folds have equal Betti numbers......Page 12 A Calabi--Yau threefold with non-Abelian fundamental group......Page 24 Algebraic Gromov--Witten invariants......Page 30 Kähler hyperbolicity and variations of Hodge structures......Page 82 Algorithms for computing intersection numbers on moduli spaces of curves, with an application to the class of the locus of Jacobians......Page 104 On some tensor representations of the Cremona group of the projective plane......Page 122 Hilbert schemes and simple singularities......Page 162 Bounds for Seshadri constants......Page 246 Degenerate double covers of the projective plane......Page 266 The geometry underlying mirror symmetry......Page 294 Duality of polarized K3 surfaces......Page 322 On symplectic invariants of algebraic varieties coming from crepant contractions......Page 338 The Bogomolov--Pantev resolution, an expository account......Page 358 Mordell--Weil lattices for higher genus fibration over a curve......Page 370 Symplectic Gromov--Witten invariants......Page 386 A generic Torelli theorem for the quintic......Page 436 Flops, Type III contractions and Gromov--Witten invariants on Calabi--Yau threefolds......Page 476 This Book Is The Outcome Of The 1996 Warwick Algebraic Geometry Euroconference, Containing 17 Survey And Research Articles Selected From The Most Outstanding Contemporary Research Topics In Algebraic Geometry. Several Of The Articles Are Expository: Among These A Beautiful Short Exposition By Paranjape Of The New And Very Simple Approach To The Resolution Of Singularities; A Detailed Essay By Ito And Nakamura On The Ubiquitous A,d,e Classification, Centred Around Simple Surface Singularities; A Discussion By Morrison Of The New Special Lagrangian Approach To Giving Geometric Foundations To Mirror Symmetry; And Two Deep, Informative Surveys By Siebert And Behrend On Gromow-witten Invariants Treating Them From The Point Of View Of Algebraic And Symplectic Geometry. The Remaining Articles Cover A Wide Cross-section Of The Most Significant Research Topics In Algebraic Geometry. This Includes Gromow-witten Invariants, Hodge Theory, Calabi-yau 3-folds, Mirror Symmetry And Classification Of Varieties. Edited By Klaus Hulek ... [et Al.]. Includes Bibliographical References. This book is the outcome of the 1996 Warwick Algebraic Geometry EuroConference, containing 17 survey and research articles selected from the most outstanding contemporary research topics in algebraic geometry. Several of the articles are expository: among these a beautiful short exposition by Paranjape of the new and very simple approach to the resolution of singularities; a detailed essay by Ito and Nakamura on the ubiquitous A, D, E classification, centred around simple surface singularities; a discussion by Morrison of the new special Lagrangian approach to giving geometric foundations to mirror symmetry; and two deep, informative surveys by Siebert and Behrend on Gromow-Witten invariants treating them from the point of view of algebraic and symplectic geometry. The remaining articles cover a wide cross-section of the most significant research topics in algebraic geometry. This includes Gromow-Witten invariants, Hodge theory, Calabi-Yau 3-folds, mirror symmetry and classification of varieties Let X and Y be two smooth projective n-dimensional algebraic varieties X and Y over C with trivial canonical line boundles.