Format:
Online-Ressource (XXVI, 602 p. 41 illus., 16 illus. in color, digital)
ISBN:
9781461464037
Series Statement:
Fields Institute Communications 67
Content:
.-Preface.-Introduction -- List of Participants -- K3 and Enriques Surfaces (S. Kondo) -- Transcendental Methods in the Study of Algebraic Cycles with a Special Emphasis on Calabi–Yau Varieties (J.D. Lewis) -- Two Lectures on the Arithmetic of K3 Surfaces (M. Schütt) -- Modularity of Calabi–Yau Varieties (N. Yui) -- Explicit Algebraic Coverings of a Pointed Torus (A. Anema, J. Top) -- Elliptic Fibrations on the Modular Surface Associated to Γ1(8) -- Universal Kummer Families over Shimura Curves (A. Besser, R. Livné) -- Numerical Trivial Automorphisms of Enriques Surfaces in Arbitrary Characteristic (I.V. Dolgachev) -- Picard-Fuchs Equations of Special One-Parameter Families of Invertible Polynomials (S. Gährs) -- A Structure Theorem for Fibrations on Delsarte Surfaces (B. Heijne, R. Kloosterman) -- Fourier–Mukai Partners and Polarised K3 Surfaces (K. Hulek, D. Ploog) -- On a Family of K3 Surfaces with S4 Symmetry (D. Karp, J. Lewish, D. Moore, D. Skjorshammer, U. Whitcher) -- K1ind of Elliptically Fibered K3 Surfaces (M. Kerr) -- A Note About Special Cycles on Moduli Spaces of K3 Surfaces (S. Kudla) -- Enriques Surfaces of Hutchinson–Göpel Type and Mathieu Automorphisms (S. Mukai, H. Ohashi) -- Quartic K3 Surfaces and Cremona Transformations (K. Oguiso) -- Invariants of Regular Models of the Product of Two Elliptical Curves at a Place of Multiplicative Reduction (C. Schoen) -- Dynamics of Special Points on Intermediate Jacobians (X. Chen, J.D. Lewis) -- Calabi–Yau Conifold Expansions (S. Cynk, D. van Straten) -- Quadratic Twists of Rigid Calabi–Yau Threefolds over Q (F.Q. Gouvêa, I. Kimming, N. Yui) -- Counting Sheaves on Calabi–Yau and Abelian Threefolds (M.G. Gulbrandsen) -- The Serge Cubic and Borcherds Products (S. Kondo) -- Quadi-Modular Forms Attached to Hodge Structures (H. Movasati) -- The Zero Locus of the Infinitesimal Invariable (G. Pearlstein, Ch. Schnell).
Content:
In recent years, research in K3 surfaces and Calabi–Yau varieties has seen spectacular progress from both the arithmetic and geometric points of view, which in turn continues to have a huge influence and impact in theoretical physics—in particular, in string theory. The workshop on Arithmetic and Geometry of K3 surfaces and Calabi–Yau threefolds, held at the Fields Institute (August 16–25, 2011), aimed to give a state-of-the-art survey of these new developments. This proceedings volume includes a representative sampling of the broad range of topics covered by the workshop. While the subjects range from arithmetic geometry through algebraic geometry and differential geometry to mathematical physics, the papers are naturally related by the common theme of Calabi–Yau varieties. With the large variety of branches of mathematics and mathematical physics touched upon, this area reveals many deep connections between subjects previously considered unrelated. Unlike most other conferences, the 2011 Calabi–Yau workshop started with three days of introductory lectures. A selection of four of these lectures is included in this volume. These lectures can be used as a starting point for graduate students and other junior researchers, or as a guide to the subject.
Note:
Description based upon print version of record
,
Preface; Introduction; List of Participants; Contents; Part I Introductory Lectures; K3 and Enriques Surfaces; 1 Introduction; 2 Lattices; 2.1 Definition; 2.2 Examples; 2.3 Unimodular Lattices; 2.4 Proposition; 2.5 Proposition; 2.6 Discriminant Quadratic Form; 2.7 Overlattices; 2.8 Proposition; 2.9 Examples; 2.10 Primitive Embeddings; 2.11 Proposition; 2.12 Corollary; 2.13 Example; 2.14 Corollary; 2.15 Corollary; 2.16 Theorem ([30]); 3 Periods of K3 and Enriques Surfaces; 3.1 Periods of K3 Surfaces; 3.2 Periods of Enriques Surfaces; 3.3 Remark; 3.4 Remark; 3.5 Example; 4 Automorphisms
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4.1 Torelli Type Theorem and the Group of Automorphisms for an Algebraic K3 Surface4.2 Theorem ([35]); 4.3 Theorem ([35]); 4.4 Corollary; 4.5 The Leech Lattice and the Group of Automorphisms of a Generic Jacobian Kummer Surface; 4.6 Theorem ([10], Chap.27); 4.7 Proposition ([4]); 4.8 Finite Groups of Automorphisms of K3 Surfaces; 4.9 Proposition ([29]); 4.10 Proposition ([29]); 4.11 Theorem ([28]); 4.12 Automorphisms of Enriques Surfaces; 4.13 Theorem ([2,31], Theorem 10.1.2); 5 Borcherds Products; 5.1 Theorem ([7]); 5.2 Example ([5]); 5.3 Example ([6,7]); 5.4 Example ([15,25]); References
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Transcendental Methods in the Study of Algebraic Cycles with a Special Emphasis on Calabi-Yau Varieties1 Introduction; 2 Notation; 3 Some Hodge Theory; 3.4 Formalism of Mixed Hodge Structures; 4 Algebraic Cycles; 4.6 Generalized Cycles; 5 A Short Detour via Milnor K-Theory; 5.1 The Gersten-Milnor Complex; 6 Hypercohomology; 7 Deligne Cohomology; 7.6 Alternate Take on Deligne Cohomology; 7.8 Deligne-Beilinson Cohomology; 8 Examples of Hr-mZar(X,KMr,X) and Corresponding Regulators; 8.1 Case m=0 and CY Threefolds; 8.5 Deligne Cohomology and Normal Functions; 8.9 Case m=1 and K3 Surfaces
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8.18 Torsion Indecomposables8.21 Case m=2 and Elliptic Curves; 8.22 Constructing K2(X) Classes on Elliptic Curves X; References; Two Lectures on the Arithmetic of K3 Surfaces; 1 Introduction; 2 Motivation: Rational Points on Algebraic Curves; 3 K3 Surfaces and Rational Points; 4 Elliptic K3 Surfaces; 5 Picard Number One; 6 Computation of Picard Numbers; 7 K3 Surfaces of Picard Number One; 7.1 van Luijk's Approach; 7.2 Kloosterman's Improvement; 7.3 Elsenhans-Jahnel's Work; 7.4 Outlook; 7.5 Feasibility; 8 Hasse Principle for K3 Surfaces; 9 Rational Curves on K3 Surfaces
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10 Isogeny Notion for K3 Surfaces11 Singular K3 Surfaces; 11.1 Torelli Theorem for Singular K3 Surfaces; 11.2 Surjectivity of the Period Map; 11.3 Singular Abelian Surfaces; 12 Shioda-Inose Structures; 13 Mordell-Weil Ranks of Elliptic K3 Surfaces; 14 Fields of Definition of Singular K3 Surfaces; 14.1 Mordell-Weil Ranks Over Q; 15 Modularity of Singular K3 Surfaces; References; Modularity of Calabi-Yau Varieties:2011 and Beyond; 1 Introduction; 1.1 Brief History Since 2003; 1.2 Plan of Lectures; 1.3 Disclaimer; 1.4 Calabi-Yau Varieties: Definition
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2 The Modularity of Galois Representations of Calabi-Yau Varieties (or Motives) Over Q
Additional Edition:
ISBN 9781461464020
Additional Edition:
Druckausg. Arithmetic and geometry of k3 surfaces and Calabi-Yau threefolds New York, NY [u.a.] : Springer [u.a.], 2013 ISBN 1461464021
Additional Edition:
ISBN 9781461464020
Language:
English
Subjects:
Mathematics
Keywords:
Calabi-Yau-Mannigfaltigkeit
;
K 3- Fläche
;
Calabi-Yau-Mannigfaltigkeit
;
K 3- Fläche
;
Konferenzschrift
DOI:
10.1007/978-1-4614-6403-7
URL:
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