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

• Record Nr.: UNINA9910962812303321
• Autore: Comparin Paola
• Pubbl/distr/stampa: Providence : , : American Mathematical Society, , 2021; ©2021
• ISBN: 9781470464226; 1470464225
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (294 pages)
• Collana: Contemporary Mathematics ; ; v.766
• Classificazione: 14H5530Fxx14Kxx14K2214H4014C3014J3214H3714J5014L30
• Altri autori (Persone): EstevesEduardo; LangeHerbert
• Disciplina: 516.3/5
• Soggetti: Geometry, Algebraic; Curves, Algebraic; Moduli theory; Symmetry (Mathematics); Algebraic varieties; Algebraic geometry -- Curves -- Riemann surfaces; Weierstrass points; gap sequences; Functions of a complex variable -- Riemann surfaces; Algebraic geometry -- Abelian varieties and schemes; Algebraic geometry -- Abelian varieties and schemes -- Complex multiplication; Algebraic geometry -- Curves -- Jacobians, Prym varieties; Algebraic geometry -- Cycles and subschemes -- Transcendental methods, Hodge theory, Hodge conjecture; Algebraic geometry -- Surfaces and higher-dimensional varieties -- Calabi-Yau manifolds; Algebraic geometry -- Curves -- Automorphisms; Algebraic geometry -- Surfaces and higher-dimensional varieties -- Automorphisms of surfaces and higher-dimensional varieties; Algebraic geometry -- Algebraic groups -- Group actions on varieties or schemes (quotients)
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: 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 -- Back Cover.
• Sommario/riassunto: Articles in this volume are based on lectures given at three conferences on Geometry at the Frontier, held at the Universidad de la Frontera, Pucón, Chile in 2016, 2017, and 2018.The papers cover recent developments on the theory of algebraic varieties--in particular, of their automorphism groups and moduli spaces. They will be of interest to anyone working in the area, as well as young mathematicians and students interested in complex and algebraic geometry.