K3 Surfaces and Their Moduli, Faber Carel, Farkas Gavril, Van Der Geer Gerard

Автор: Carel Faber; Gavril Farkas; Gerard van der Geer
Название: K3 Surfaces and Their Moduli
ISBN: 3319299581 ISBN-13(EAN): 9783319299587
Издательство: Springer
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This book provides an overview of the latest developments concerning the moduli of K3 surfaces. It is aimed at algebraic geometers, but is also of interest to number theorists and theoretical physicists, and continues the tradition of related volumes like "The Moduli Space of Curves" and "Moduli of Abelian Varieties," which originated from conferences on the islands Texel and Schiermonnikoog and which have become classics.

K3 surfaces and their moduli form a central topic in algebraic geometry and arithmetic geometry, and have recently attracted a lot of attention from both mathematicians and theoretical physicists. Advances in this field often result from mixing sophisticated techniques from algebraic geometry, lattice theory, number theory, and dynamical systems. The topic has received significant impetus due to recent breakthroughs on the Tate conjecture, the study of stability conditions and derived categories, and links with mirror symmetry and string theory. At the same time, the theory of irreducible holomorphic symplectic varieties, the higher dimensional analogues of K3 surfaces, has become a mainstream topic in algebraic geometry.

Contributors: S. Boissi re, A. Cattaneo, I. Dolgachev, V. Gritsenko, B. Hassett, G. Heckman, K. Hulek, S. Katz, A. Klemm, S. Kondo, C. Liedtke, D. Matsushita, M. Nieper-Wisskirchen, G. Oberdieck, K. Oguiso, R. Pandharipande, S. Rieken, A. Sarti, I. Shimada, R. P. Thomas, Y. Tschinkel, A. Verra, C. Voisin.

Автор: Vladimir Fock; Andrey Marshakov; Florent Schaffhau
Название: Geometry and Quantization of Moduli Spaces
ISBN: 3319335774 ISBN-13(EAN): 9783319335773
Издательство: Springer
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Цена: 27940.00 T
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Описание: It presents both background information and recent developments on selected topics that are experiencing extraordinary growth within the broad research area of geometry and quantization of moduli spaces.

Автор: Roman Bezrukavnikov, Alexander Braverman, Zhiwei Yun
Название: Geometry of Moduli Spaces and Representation Theory
ISBN: 1470435748 ISBN-13(EAN): 9781470435745
Издательство: Mare Nostrum (Eurospan)
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Описание: This book is based on lectures given at the Graduate Summer School of the 2015 Park City Mathematics Institute program ``Geometry of moduli spaces and representation theory'', and is devoted to several interrelated topics in algebraic geometry, topology of algebraic varieties, and representation theory.Geometric representation theory is a young but fast developing research area at the intersection of these subjects. An early profound achievement was the famous conjecture by Kazhdan-Lusztig about characters of highest weight modules over a complex semi-simple Lie algebra, and its subsequent proof by Beilinson-Bernstein and Brylinski-Kashiwara. Two remarkable features of this proof have inspired much of subsequent development: intricate algebraic data turned out to be encoded in topological invariants of singular geometric spaces, while proving this fact required deep general theorems from algebraic geometry.Another focus of the program was enumerative algebraic geometry. Recent progress showed the role of Lie theoretic structures in problems such as calculation of quantum cohomology, K-theory, etc. Although the motivation and technical background of these constructions is quite different from that of geometric Langlands duality, both theories deal with topological invariants of moduli spaces of maps from a target of complex dimension one. Thus they are at least heuristically related, while several recent works indicate possible strong technical connections.The main goal of this collection of notes is to provide young researchers and experts alike with an introduction to these areas of active research and promote interaction between the two related directions.

Автор: Nicole Marc-Hubert
Название: Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces: Hyperbolicity in Montrйal
ISBN: 3030498638 ISBN-13(EAN): 9783030498634
Издательство: Springer
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Цена: 46570.00 T
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Описание: Lastly, part four introduces the relation between physics and information theory, which constitutes a new frontier in fundamental research.The book includes step-by-step exercises, with solutions, to help readers to gain a fuller understanding of the subjects, and also features a series of appendices providing useful mathematical formulae.

Автор: Brambila-Paz
Название: Moduli Spaces
ISBN: 1107636388 ISBN-13(EAN): 9781107636385
Издательство: Cambridge Academ
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Цена: 64410.00 T
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Описание: Moduli theory represents a significant topic of modern mathematical research with strong connections to many areas of mathematics (including geometry, topology and number theory) and other disciplines such as theoretical physics. This book presents articles on both fundamental material and advanced research topics, accessible at the graduate level and above.

Автор: Paul Hacking; Radu Laza; Dragos Oprea; Gilberto Bi
Название: Compactifying Moduli Spaces
ISBN: 3034809204 ISBN-13(EAN): 9783034809207
Издательство: Springer
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Цена: 23280.00 T
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Описание: This book focusses on a large class of objects in moduli theory and provides different perspectives from which compactifications of moduli spaces may be investigated. Three contributions give an insight on particular aspects of moduli problems.

Автор: Auel Asher, Hassett Brendan, Vбrilly-Alvarado Anthony
Название: Brauer Groups and Obstruction Problems: Moduli Spaces and Arithmetic
ISBN: 3319836013 ISBN-13(EAN): 9783319836010
Издательство: Springer
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Цена: 139750.00 T
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The Brauer group is not a derived invariant.- Twisted derived equivalences for affine schemes.- Rational points on twisted K3 surfaces and derived equivalences.- Universal unramified cohomology of cubic fourfolds containing a plane.- Universal spaces for unramified Galois cohomology.- Rational points on K3 surfaces and derived equivalence.- Unramified Brauer classes on cyclic covers of the projective plane.- Arithmetically Cohen-Macaulay bundles on cubic fourfolds containing a plane.- Brauer groups on K3 surfaces and arithmetic applications.- On a local-global principle for H³ of function fields of surfaces over a finite field.- Cohomology and the Brauer group of double covers.

Автор: Leticia Brambila Paz; Ciro Ciliberto; Eduardo Este
Название: Moduli of Curves
ISBN: 3319594850 ISBN-13(EAN): 9783319594859
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Цена: 55890.00 T
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Описание: Foreword.- Melody Chan: Lectures on Tropical Curves and their Moduli Spaces.- Paolo Cascini.- Lecture notes for the CIMPA school.- Olivier Debarre: Higher-Dimensional Varieties.- Gavril Farkas: Progress on Syzygies of algebraic Curves.- Emanuele Macrн, Benjamin Schmidt: Lectures on Bridgeland Stability.- Edoardo Sernesi: Algebraic Curves and their Moduli.

Автор: Mizera Sebastian
Название: Aspects of Scattering Amplitudes and Moduli Space Localization
ISBN: 3030530094 ISBN-13(EAN): 9783030530099
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Цена: 121110.00 T
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Описание: Chapter1: Introduction.- Chapter2: Intersection Numbers of Twisted Di erential Forms.- Chapter3: Recursion Relations from Braid Matrices.- Chapter4: Further Examples of Intersection Numbers.- Chapter5: Conclusion.

Автор: Codogni Giulio, Dervan Ruadhaн, Viviani Filippo
Название: Moduli of K-Stable Varieties
ISBN: 3030131602 ISBN-13(EAN): 9783030131609
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Цена: 130430.00 T
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Описание: and develop tropical aspects of the moduli space of curves, the singularity theory necessary for higher dimensional moduli theory, and the existence of minimal models.

Автор: Kieran G. O`Grady
Название: Moduli of Double EPW-Sextics
ISBN: 1470416964 ISBN-13(EAN): 9781470416966
Издательство: Mare Nostrum (Eurospan)
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Цена: 92400.00 T
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Описание: The author studies the GIT quotient of the symplectic grassmannian parametrizing lagrangian subspaces of $\bigwedge^3{\mathbb C}^6$ modulo the natural action of $\mathrm{SL}_6$, call it $\mathfrak{M}$. This is a compactification of the moduli space of smooth double EPW-sextics and hence birational to the moduli space of HK $4$-folds of Type $K3^{[2]}$ polarized by a divisor of square $2$ for the Beauville-Bogomolov quadratic form. The author will determine the stable points. His work bears a strong analogy with the work of Voisin, Laza and Looijenga on moduli and periods of cubic $4$-folds.

Автор: Mumford David
Название: Selected Papers I: On the Classification of Varieties and Moduli Spaces
ISBN: 1493995359 ISBN-13(EAN): 9781493995356
Издательство: Springer
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Цена: 60550.00 T
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Описание: Mumford is a well-known mathematician and winner of the Fields Medal, the highest honor available in mathematics. Many of these papers are currently unavailable, and the commentaries by Gieseker, Lange, Viehweg and Kempf are being published here for the first time.