Geometry Of Moduli

Geometry Of Moduli Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Geometry Of Moduli book. This book definitely worth reading, it is an incredibly well-written.

Geometry of Moduli

Jan Arthur Christophersen,Kristian Ranestad
Geometry of Moduli Book PDF

Author : Jan Arthur Christophersen,Kristian Ranestad
Publisher : Springer
Page : 0 pages
File Size : 54,8 Mb
Release : 2018-11-24
Category : Mathematics
ISBN : 3319948806

Get Book

Geometry of Moduli by Jan Arthur Christophersen,Kristian Ranestad Pdf

The proceedings from the Abel Symposium on Geometry of Moduli, held at Svinøya Rorbuer, Svolvær in Lofoten, in August 2017, present both survey and research articles on the recent surge of developments in understanding moduli problems in algebraic geometry. Written by many of the main contributors to this evolving subject, the book provides a comprehensive collection of new methods and the various directions in which moduli theory is advancing. These include the geometry of moduli spaces, non-reductive geometric invariant theory, birational geometry, enumerative geometry, hyper-kähler geometry, syzygies of curves and Brill-Noether theory and stability conditions. Moduli theory is ubiquitous in algebraic geometry, and this is reflected in the list of moduli spaces addressed in this volume: sheaves on varieties, symmetric tensors, abelian differentials, (log) Calabi-Yau varieties, points on schemes, rational varieties, curves, abelian varieties and hyper-Kähler manifolds.

The Geometry of Moduli Spaces of Sheaves

Daniel Huybrechts,Manfred Lehn
The Geometry of Moduli Spaces of Sheaves Book PDF

Author : Daniel Huybrechts,Manfred Lehn
Publisher : Cambridge University Press
Page : 345 pages
File Size : 45,9 Mb
Release : 2010-05-27
Category : Mathematics
ISBN : 9781139485821

Get Book

The Geometry of Moduli Spaces of Sheaves by Daniel Huybrechts,Manfred Lehn Pdf

This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.

Birational Geometry and Moduli Spaces

Elisabetta Colombo,Barbara Fantechi,Paola Frediani,Donatella Iacono,Rita Pardini
Birational Geometry and Moduli Spaces Book PDF

Author : Elisabetta Colombo,Barbara Fantechi,Paola Frediani,Donatella Iacono,Rita Pardini
Publisher : Springer Nature
Page : 200 pages
File Size : 41,7 Mb
Release : 2020-02-25
Category : Mathematics
ISBN : 9783030371142

Get Book

Birational Geometry and Moduli Spaces by Elisabetta Colombo,Barbara Fantechi,Paola Frediani,Donatella Iacono,Rita Pardini Pdf

This volume collects contributions from speakers at the INdAM Workshop “Birational Geometry and Moduli Spaces”, which was held in Rome on 11–15 June 2018. The workshop was devoted to the interplay between birational geometry and moduli spaces and the contributions of the volume reflect the same idea, focusing on both these areas and their interaction. In particular, the book includes both surveys and original papers on irreducible holomorphic symplectic manifolds, Severi varieties, degenerations of Calabi-Yau varieties, uniruled threefolds, toric Fano threefolds, mirror symmetry, canonical bundle formula, the Lefschetz principle, birational transformations, and deformations of diagrams of algebras. The intention is to disseminate the knowledge of advanced results and key techniques used to solve open problems. The book is intended for all advanced graduate students and researchers interested in the new research frontiers of birational geometry and moduli spaces.

Geometry of Moduli Spaces and Representation Theory

Roman Bezrukavnikov,Alexander Braverman,Zhiwei Yun
Geometry of Moduli Spaces and Representation Theory Book PDF

Author : Roman Bezrukavnikov,Alexander Braverman,Zhiwei Yun
Publisher : American Mathematical Soc.
Page : 436 pages
File Size : 42,6 Mb
Release : 2017-12-15
Category : Algebraic varieties
ISBN : 9781470435745

Get Book

Geometry of Moduli Spaces and Representation Theory by Roman Bezrukavnikov,Alexander Braverman,Zhiwei Yun Pdf

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.

Moduli of Curves

Joe Harris,Ian Morrison
Moduli of Curves Book PDF

Author : Joe Harris,Ian Morrison
Publisher : Springer Science & Business Media
Page : 381 pages
File Size : 51,7 Mb
Release : 2006-04-06
Category : Mathematics
ISBN : 9780387227375

Get Book

Moduli of Curves by Joe Harris,Ian Morrison Pdf

A guide to a rich and fascinating subject: algebraic curves and how they vary in families. Providing a broad but compact overview of the field, this book is accessible to readers with a modest background in algebraic geometry. It develops many techniques, including Hilbert schemes, deformation theory, stable reduction, intersection theory, and geometric invariant theory, with the focus on examples and applications arising in the study of moduli of curves. From such foundations, the book goes on to show how moduli spaces of curves are constructed, illustrates typical applications with the proofs of the Brill-Noether and Gieseker-Petri theorems via limit linear series, and surveys the most important results about their geometry ranging from irreducibility and complete subvarieties to ample divisors and Kodaira dimension. With over 180 exercises and 70 figures, the book also provides a concise introduction to the main results and open problems about important topics which are not covered in detail.

The Moduli Space of Curves

Robert H. Dijkgraaf,Carel Faber,Gerard B.M. van der Geer
The Moduli Space of Curves Book PDF

Author : Robert H. Dijkgraaf,Carel Faber,Gerard B.M. van der Geer
Publisher : Springer Science & Business Media
Page : 570 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461242642

Get Book

The Moduli Space of Curves by Robert H. Dijkgraaf,Carel Faber,Gerard B.M. van der Geer Pdf

The moduli space Mg of curves of fixed genus g – that is, the algebraic variety that parametrizes all curves of genus g – is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory.

Moduli Spaces

Leticia Brambila,Oscar García-Prada,Peter Newstead,Richard P. Thomas
Moduli Spaces Book PDF

Author : Leticia Brambila,Oscar García-Prada,Peter Newstead,Richard P. Thomas
Publisher : Cambridge University Press
Page : 347 pages
File Size : 49,8 Mb
Release : 2014-03-13
Category : Mathematics
ISBN : 9781107636385

Get Book

Moduli Spaces by Leticia Brambila,Oscar García-Prada,Peter Newstead,Richard P. Thomas Pdf

A graduate-level introduction to some of the important contemporary ideas and problems in the theory of moduli spaces.

Computers, Rigidity, and Moduli

Shmuel Weinberger
Computers Rigidity and Moduli Book PDF

Author : Shmuel Weinberger
Publisher : Princeton University Press
Page : 204 pages
File Size : 46,5 Mb
Release : 2005
Category : Computers
ISBN : 0691118892

Get Book

Computers, Rigidity, and Moduli by Shmuel Weinberger Pdf

This book is the first to present a new area of mathematical research that combines topology, geometry, and logic. Shmuel Weinberger seeks to explain and illustrate the implications of the general principle, first emphasized by Alex Nabutovsky, that logical complexity engenders geometric complexity. He provides applications to the problem of closed geodesics, the theory of submanifolds, and the structure of the moduli space of isometry classes of Riemannian metrics with curvature bounds on a given manifold. Ultimately, geometric complexity of a moduli space forces functions defined on that space to have many critical points, and new results about the existence of extrema or equilibria follow. The main sort of algorithmic problem that arises is recognition: is the presented object equivalent to some standard one? If it is difficult to determine whether the problem is solvable, then the original object has doppelgängers--that is, other objects that are extremely difficult to distinguish from it. Many new questions emerge about the algorithmic nature of known geometric theorems, about "dichotomy problems," and about the metric entropy of moduli space. Weinberger studies them using tools from group theory, computability, differential geometry, and topology, all of which he explains before use. Since several examples are worked out, the overarching principles are set in a clear relief that goes beyond the details of any one problem.

Quasi-projective Moduli for Polarized Manifolds

Eckart Viehweg
Quasi projective Moduli for Polarized Manifolds Book PDF

Author : Eckart Viehweg
Publisher : Springer Science & Business Media
Page : 329 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642797453

Get Book

Quasi-projective Moduli for Polarized Manifolds by Eckart Viehweg Pdf

The concept of moduli goes back to B. Riemann, who shows in [68] that the isomorphism class of a Riemann surface of genus 9 ~ 2 depends on 3g - 3 parameters, which he proposes to name "moduli". A precise formulation of global moduli problems in algebraic geometry, the definition of moduli schemes or of algebraic moduli spaces for curves and for certain higher dimensional manifolds have only been given recently (A. Grothendieck, D. Mumford, see [59]), as well as solutions in some cases. It is the aim of this monograph to present methods which allow over a field of characteristic zero to construct certain moduli schemes together with an ample sheaf. Our main source of inspiration is D. Mumford's "Geometric In variant Theory". We will recall the necessary tools from his book [59] and prove the "Hilbert-Mumford Criterion" and some modified version for the stability of points under group actions. As in [78], a careful study of positivity proper ties of direct image sheaves allows to use this criterion to construct moduli as quasi-projective schemes for canonically polarized manifolds and for polarized manifolds with a semi-ample canonical sheaf.

Moduli Spaces and Vector Bundles

Steve Bradlow
Moduli Spaces and Vector Bundles Book PDF

Author : Steve Bradlow
Publisher : Cambridge University Press
Page : 516 pages
File Size : 47,5 Mb
Release : 2009-05-21
Category : Mathematics
ISBN : 9780521734714

Get Book

Moduli Spaces and Vector Bundles by Steve Bradlow Pdf

Coverage includes foundational material as well as current research, authored by top specialists within their fields.

Geometry of Moduli

Jan Arthur Christophersen,Kristian Ranestad
Geometry of Moduli Book PDF

Author : Jan Arthur Christophersen,Kristian Ranestad
Publisher : Springer
Page : 326 pages
File Size : 50,7 Mb
Release : 2018-11-24
Category : Mathematics
ISBN : 9783319948812

Get Book

Geometry of Moduli by Jan Arthur Christophersen,Kristian Ranestad Pdf

The proceedings from the Abel Symposium on Geometry of Moduli, held at Svinøya Rorbuer, Svolvær in Lofoten, in August 2017, present both survey and research articles on the recent surge of developments in understanding moduli problems in algebraic geometry. Written by many of the main contributors to this evolving subject, the book provides a comprehensive collection of new methods and the various directions in which moduli theory is advancing. These include the geometry of moduli spaces, non-reductive geometric invariant theory, birational geometry, enumerative geometry, hyper-kähler geometry, syzygies of curves and Brill-Noether theory and stability conditions. Moduli theory is ubiquitous in algebraic geometry, and this is reflected in the list of moduli spaces addressed in this volume: sheaves on varieties, symmetric tensors, abelian differentials, (log) Calabi-Yau varieties, points on schemes, rational varieties, curves, abelian varieties and hyper-Kähler manifolds.

Moduli Spaces of Riemannian Metrics

Wilderich Tuschmann,David J. Wraith
Moduli Spaces of Riemannian Metrics Book PDF

Author : Wilderich Tuschmann,David J. Wraith
Publisher : Springer
Page : 123 pages
File Size : 43,8 Mb
Release : 2015-10-14
Category : Mathematics
ISBN : 9783034809481

Get Book

Moduli Spaces of Riemannian Metrics by Wilderich Tuschmann,David J. Wraith Pdf

This book studies certain spaces of Riemannian metrics on both compact and non-compact manifolds. These spaces are defined by various sign-based curvature conditions, with special attention paid to positive scalar curvature and non-negative sectional curvature, though we also consider positive Ricci and non-positive sectional curvature. If we form the quotient of such a space of metrics under the action of the diffeomorphism group (or possibly a subgroup) we obtain a moduli space. Understanding the topology of both the original space of metrics and the corresponding moduli space form the central theme of this book. For example, what can be said about the connectedness or the various homotopy groups of such spaces? We explore the major results in the area, but provide sufficient background so that a non-expert with a grounding in Riemannian geometry can access this growing area of research.

Algebraic Curves

Maxim E. Kazaryan,Sergei K. Lando,Victor V. Prasolov
Algebraic Curves Book PDF

Author : Maxim E. Kazaryan,Sergei K. Lando,Victor V. Prasolov
Publisher : Springer
Page : 231 pages
File Size : 54,7 Mb
Release : 2019-01-21
Category : Mathematics
ISBN : 9783030029432

Get Book

Algebraic Curves by Maxim E. Kazaryan,Sergei K. Lando,Victor V. Prasolov Pdf

This book offers a concise yet thorough introduction to the notion of moduli spaces of complex algebraic curves. Over the last few decades, this notion has become central not only in algebraic geometry, but in mathematical physics, including string theory, as well. The book begins by studying individual smooth algebraic curves, including the most beautiful ones, before addressing families of curves. Studying families of algebraic curves often proves to be more efficient than studying individual curves: these families and their total spaces can still be smooth, even if there are singular curves among their members. A major discovery of the 20th century, attributed to P. Deligne and D. Mumford, was that curves with only mild singularities form smooth compact moduli spaces. An unexpected byproduct of this discovery was the realization that the analysis of more complex curve singularities is not a necessary step in understanding the geometry of the moduli spaces. The book does not use the sophisticated machinery of modern algebraic geometry, and most classical objects related to curves – such as Jacobian, space of holomorphic differentials, the Riemann-Roch theorem, and Weierstrass points – are treated at a basic level that does not require a profound command of algebraic geometry, but which is sufficient for extending them to vector bundles and other geometric objects associated to moduli spaces. Nevertheless, it offers clear information on the construction of the moduli spaces, and provides readers with tools for practical operations with this notion. Based on several lecture courses given by the authors at the Independent University of Moscow and Higher School of Economics, the book also includes a wealth of problems, making it suitable not only for individual research, but also as a textbook for undergraduate and graduate coursework

An Introduction to Invariants and Moduli

Shigeru Mukai
An Introduction to Invariants and Moduli Book PDF

Author : Shigeru Mukai
Publisher : Cambridge University Press
Page : 528 pages
File Size : 44,9 Mb
Release : 2003-09-08
Category : Mathematics
ISBN : 0521809061

Get Book

An Introduction to Invariants and Moduli by Shigeru Mukai Pdf

Sample Text

Moduli Spaces of Riemann Surfaces

Benson Farb,Richard Hain,Eduard Looijenga
Moduli Spaces of Riemann Surfaces Book PDF

Author : Benson Farb,Richard Hain,Eduard Looijenga
Publisher : American Mathematical Soc.
Page : 371 pages
File Size : 52,7 Mb
Release : 2013-08-16
Category : Mathematics
ISBN : 9780821898871

Get Book

Moduli Spaces of Riemann Surfaces by Benson Farb,Richard Hain,Eduard Looijenga Pdf

Mapping class groups and moduli spaces of Riemann surfaces were the topics of the Graduate Summer School at the 2011 IAS/Park City Mathematics Institute. This book presents the nine different lecture series comprising the summer school, covering a selection of topics of current interest. The introductory courses treat mapping class groups and Teichmüller theory. The more advanced courses cover intersection theory on moduli spaces, the dynamics of polygonal billiards and moduli spaces, the stable cohomology of mapping class groups, the structure of Torelli groups, and arithmetic mapping class groups. The courses consist of a set of intensive short lectures offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The book should be a valuable resource for graduate students and researchers interested in the topology, geometry and dynamics of moduli spaces of Riemann surfaces and related topics. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.