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08410cam a2201069 i 4500 |
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972331010 |
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OCoLC |
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20240329122006.0 |
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|a Geometry over nonclosed fields /
|c Fedor Bogomolov, Brendan Hassett, Yuri Tschinkel, editors.
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|a Cham, Switzerland :
|b Springer,
|c 2017.
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|a 1 online resource.
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|a text
|b txt
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|a computer
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|a online resource
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|a text file
|b PDF
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|a Simons Symposia,
|x 2365-9564.
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|a Online resource; title from PDF title page (SpringerLink, viewed February 20, 2017).
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|6 880-01
|a Preface; Contents; On the Kobayashi Pseudometric, Complex Automorphisms and Hyperkähler Manifolds; 1 Introduction; 2 Preliminaries; 3 (Royden -- )Kobayashi Pseudometric on Abelian Fibrations; 4 Automorphisms of Infinite Order; 5 Metric Geometry of Kobayashi Quotients; 6 Eigenvalues and Periodic Points of Hyperbolic Automorphisms; References; Lines on Cubic Hypersurfaces Over Finite Fields; 1 Introduction; 2 Definitions and Tools; 2.1 The Weil and Tate Conjectures; 2.2 The Katz Trace Formula; 2.3 The Galkin -- Shinder Formulas; 2.4 Abelian Varieties Over Finite Fields; 3 Cubic Surfaces.
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|a 4 Cubic Threefolds4.1 The Zeta Function of the Surface of Lines; 4.2 Existence of Lines on Smooth Cubic Threefolds Over Large Finite Fields; 4.3 Computing Techniques: The Bombieri -- Swinnerton-Dyer Method; 4.4 Lines on Mildly Singular Cubic Threefolds; 4.5 Examples of Cubic Threefolds; 4.6 Average Number of Lines; 5 Cubic Fourfolds; 5.1 The Zeta Function of the Fourfold of Lines; 5.2 Existence of Lines over Large Finite Fields; 5.3 Existence of Lines over Some Finite Fields; 5.4 Examples of Cubic Fourfolds; 6 Cubics of Dimensions 5 or More; References.
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|a Perverse Sheaves of Categories and Non-rationality1 Introduction; 2 Perverse Sheaves of Categories; 2.1 Definitions; 2.2 Some More Examples; 3 Deformations of Perverse Sheaves of Categories and Poisson Deformations; 3.1 Warmup: Deformations of mathbbP2; 3.2 Noncommutative Deformations of mathbbP3; 3.3 Perverse Sheaves of Categories and Elliptic Curves; 4 Landau -- Ginzburg Model Computations for Threefolds; 4.1 The LG Model of a Quartic Double Solid; 4.2 Torsion in Cohomology of the LG Model; 4.3 The Cubic Threefold; 4.4 The Quartic Double Fourfold; 4.5 Base Change and Torsion.
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|a 1.2 Morphisms to Brauer -- Severi Varieties.
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|a Based on the Simons Symposia held in 2015, the proceedings in this volume focus on rational curves on higher-dimensional algebraic varieties and applications of the theory of curves to arithmetic problems. There has been significant progress in this field with major new results, which have given new impetus to the study of rational curves and spaces of rational curves on K3 surfaces and their higher-dimensional generalizations. One main recent insight the book covers is the idea that the geometry of rational curves is tightly coupled to properties of derived categories of sheaves on K3 surfaces. The implementation of this idea led to proofs of long-standing conjectures concerning birational properties of holomorphic symplectic varieties, which in turn should yield new theorems in arithmetic. This proceedings volume covers these new insights in detail.
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|a Includes bibliographical references.
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|a Geometry, Algebraic.
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|a Algebraic fields.
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|a Algebraic stacks.
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|a Mathematics.
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|a Geometry, Algebraic.
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|a Géométrie algébrique.
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|a Corps algébriques.
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|a Algebraic geometry.
|2 bicssc.
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|a MATHEMATICS
|x Geometry
|x General.
|2 bisacsh.
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| 650 |
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|a Geometría algebraica.
|2 embne.
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| 650 |
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|a Cuerpos algebraicos.
|2 embne.
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| 650 |
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|a Algebraic stacks.
|2 fast.
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|a Algebraic fields.
|2 fast.
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| 650 |
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|a Geometry, Algebraic.
|2 fast.
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| 700 |
1 |
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|a Bogomolov, Fedor,
|d 1946-
|e editor.
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|a Hassett, Brendan,
|e editor.
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|a Tschinkel, Yuri,
|e editor.
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| 710 |
2 |
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|a SpringerLink (Online service)
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| 776 |
0 |
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|i Print version:
|t Geometry over nonclosed fields.
|d Cham, Switzerland : Springer, 2017
|z 3319497626
|z 9783319497624
|w (OCoLC)961004925.
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| 830 |
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|a Simons symposia.
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| 880 |
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|6 505-00/(S
|a 4.6 Cubic Fourfolds and Their Mirrors4.7 The General Cubic Fourfold; 4.8 Cubic Fourfolds Blown up in a Plane; 4.9 Cubic Threefolds Blown up in Two Planes; 4.10 Special Lagrangian Fibrations; 5 Hybrid Models and Filtrations; 5.1 Filtration; 5.2 Hybrid Models; 5.3 Artin--Mumford Example; 5.4 Conclusions; 5.5 Final Example; References; Divisor Classes and the Virtual Canonical Bundle for Genus 0 Maps; 1 Statement of Results; 1.1 Outline of the Article; 2 Notation for Moduli Spaces and Boundary Divisor Classes; 3 The Functor Qs; 4 Local Computations; 4.1 Computation of Qs(}s).
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|6 505-01/(S
|a 4.2 Computation of Qs(L) for Invertible Sheaves of Degree 05 Proof of Proposition 1.2; 6 Proof of Theorem 1.1; References; A Stronger Derived Torelli Theorem for K3 Surfaces; 1 Introduction; 2 Strongly Filtered Equivalences; 3 Moduli Spaces of K3 Surfaces; 4 Deformations of Autoequivalences; 5 A Remark on Reduction Types; 6 Supersingular Reduction; 7 Specialization; 8 Proof of Theorem 1.2; 9 Characteristic 0; 10 Bypassing Hodge Theory; References; Morphisms to Brauer--Severi Varieties, with Applications to Del Pezzo Surfaces; 1 Introduction; 1.1 Overview.
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