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Author | : Robert H. Dijkgraaf |
Publisher | : Springer Science & Business Media |
Total Pages | : 570 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461242649 |
Download The Moduli Space of Curves Book in PDF, ePub and Kindle
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.
Author | : Benson Farb |
Publisher | : American Mathematical Soc. |
Total Pages | : 371 |
Release | : 2013-08-16 |
Genre | : Mathematics |
ISBN | : 0821898876 |
Download Moduli Spaces of Riemann Surfaces Book in PDF, ePub and Kindle
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.
Author | : Daniel Huybrechts |
Publisher | : Cambridge University Press |
Total Pages | : 345 |
Release | : 2010-05-27 |
Genre | : Mathematics |
ISBN | : 1139485822 |
Download The Geometry of Moduli Spaces of Sheaves Book in PDF, ePub and Kindle
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.
Author | : Maxim E. Kazaryan |
Publisher | : Springer |
Total Pages | : 231 |
Release | : 2019-01-21 |
Genre | : Mathematics |
ISBN | : 3030029433 |
Download Algebraic Curves Book in PDF, ePub and Kindle
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
Author | : Leticia Brambila |
Publisher | : Cambridge University Press |
Total Pages | : 347 |
Release | : 2014-03-13 |
Genre | : Mathematics |
ISBN | : 1107636388 |
Download Moduli Spaces Book in PDF, ePub and Kindle
A graduate-level introduction to some of the important contemporary ideas and problems in the theory of moduli spaces.
Author | : Wilderich Tuschmann |
Publisher | : Springer |
Total Pages | : 127 |
Release | : 2015-10-14 |
Genre | : Mathematics |
ISBN | : 3034809484 |
Download Moduli Spaces of Riemannian Metrics Book in PDF, ePub and Kindle
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.
Author | : Martin C. Olsson |
Publisher | : Springer Science & Business Media |
Total Pages | : 286 |
Release | : 2008-08-25 |
Genre | : Mathematics |
ISBN | : 354070518X |
Download Compactifying Moduli Spaces for Abelian Varieties Book in PDF, ePub and Kindle
This volume presents the construction of canonical modular compactifications of moduli spaces for polarized Abelian varieties (possibly with level structure), building on the earlier work of Alexeev, Nakamura, and Namikawa. This provides a different approach to compactifying these spaces than the more classical approach using toroical embeddings, which are not canonical. There are two main new contributions in this monograph: (1) The introduction of logarithmic geometry as understood by Fontaine, Illusie, and Kato to the study of degenerating Abelian varieties; and (2) the construction of canonical compactifications for moduli spaces with higher degree polarizations based on stack-theoretic techniques and a study of the theta group.
Author | : Elisabetta Colombo |
Publisher | : Springer Nature |
Total Pages | : 200 |
Release | : 2020-02-25 |
Genre | : Mathematics |
ISBN | : 303037114X |
Download Birational Geometry and Moduli Spaces Book in PDF, ePub and Kindle
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.
Author | : Steve Bradlow |
Publisher | : Cambridge University Press |
Total Pages | : 516 |
Release | : 2009-05-21 |
Genre | : Mathematics |
ISBN | : 0521734711 |
Download Moduli Spaces and Vector Bundles Book in PDF, ePub and Kindle
Coverage includes foundational material as well as current research, authored by top specialists within their fields.
Author | : Joe Harris |
Publisher | : Springer Science & Business Media |
Total Pages | : 381 |
Release | : 2006-04-06 |
Genre | : Mathematics |
ISBN | : 0387227377 |
Download Moduli of Curves Book in PDF, ePub and Kindle
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.