Geometry at the Frontier : Symmetries and Moduli Spaces of Algebraic Varieties.

Cover
Title page
Contents
Preface
Lower and upper bounds for some generalized arcs
Introduction
1. Basic definitions and background material
2. Some upper bounds for _{ }(2, )
3. Some lower bounds for (2, ), ᵥ(2, ) and _{ }(2, )
Appendix: Magma programs
Acknowledgments
References
Symmetries of order eight on K3 surfaces without high genus curves in the fixed locus
Introduction
1. Basic facts
2. The fixed locus
3. The classification
4. Elliptic fibrations
5. Examples
Acknowledgments
References
A decomposition of the Jacobian of a Humbert-Edge curve
1. Introduction
2. Main theorem
3. Proof of the main theorem
4. Geometric description of the decomposition of _{ }
Acknowledgements
References
Connections on central extensions, lifting gerbes, and finite-dimensional obstruction vanishing
Introduction
1. Preliminaries
2. Distortion of equivariant connections
3. Central extensions
4. Lifting gerbes and connective structures
5. Vanishing of Neeb's obstructions
References
Some algebraic and geometric properties of hyper-Kähler fourfold symmetries
1. Introduction
2. Prime order isometries of integral lattices
3. Order five symmetries of the Hilbert square of a K3 surface
4. Natural automorphisms of Kummer fourfolds
Acknowledgments
References
On the existence of groups of automorphisms of compact Riemann and Klein surfaces
1. Introduction
2. Preliminaries
3. Finite groups as full automorphism groups
4. Surface normal subgroups of finite index
5. Necessary and sufficient conditions for the existence of a finite group action
6. Conditions for the existence of a finite full group action
References
Hyperbolic structures for Artin-Tits groups of spherical type
1. Introduction
2. Preliminaries.

3. Hyperbolic structures for ℬ_{ +1}
4. Generalizing to Artin-Tits groups of spherical type
References
Linear stability for line bundles over curves
1. Introduction
2. Extensions of line bundles
3. Linear stability and stability of Syzygy bundle
References
The contribution of W. L. Edge to the study of Humbert's curves
1. Introduction
2. Edge's approach to Humbert's curves
3. Chords and projections
4. Differentials and equations for ℋ
5. Planar representation of ᵢ
6. Moduli and degenerations
References
Deformations of noncompact Calabi-Yau manifolds, families and diamonds
1. Deformations of complex structures
2. Deformations of noncompact manifolds
3. Hyperkähler families
4. Adjoint orbits and cotangent bundles
5. Diamonds
6. Acknowledgments
References
A brute force computer aided proof of an existence result about extremal hyperbolic surfaces
1. Introduction
2. The main result
3. The brute force construction
4. Full details of the construction for the case =14.
5. End of the proof of Theorem 2.1
Acknowledgment
References
Complex surfaces with mutually non-biholomorphic universal covers
1. Introduction and statement of results
2. Preliminaries
3. Proof of the Theorem
4. Proof of the Proposition
Acknowledgments
References
Hodge theory and moduli
Outline
References
Constructing Jacobian varieties with many elliptic curves
1. Introduction
2. Some preliminaries
3. The constructions
4. Proof of Theorems 3 and 6
5. Explicit examples
Acknowledgments
References
Weil's Galois descent theorem from a computational point of view
1. Introduction
2. Preliminaries
3. Constructive proof of Weil's Galois descent theorem
4. Applications to complex algebraic varieties and field of moduli.

5. An Explicit Example: A curve of genus 5
References
Subcovers of curves and moduli spaces
1. Introduction
2. Humbert surfaces
3. The geometry of Humbert surfaces
4. Connectedness properties
5. Intersections of Humbert surfaces
6. The refined Humbert invariant
7. Generalized Humbert schemes
8. Special quadratic forms
9. The components of ( )
10. The structure of ( )
11. Method of proof
Acknowledgment
References
Algebraic geometry and convolutional codes
1. Introduction
2. Convolutional codes. Classification and free distance
3. Convolutional Goppa codes
4. Further applications and future work
References
Adelic and idelic pairings related to Weil reciprocity on algebraic curves
1. Introduction
2. Adeles, ideles, and the function field
3. Reciprocity pairing on ideles
4. The Main Quotient (Σ_{ }*)^{\pperp}/Σ_{ }* -Topology
5. The Main Quotient (Σ_{ }*)^{\pperp}/Σ_{ }* -Geometry
6. Applications
Acknowledgments
References
Remarks on the size of the Tamagawa product
1. Tamagawa factors
2. Notation and preliminaries
3. Smallness of the Tamagawa factor
4. Diophantine consequences
References
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