Geometry Of Moduli PDF Download
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| 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 | : 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 | : Roman Bezrukavnikov |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 449 |
| Release | : 2017-12-15 |
| Genre | : Mathematics |
| ISBN | : 1470435748 |
Download Geometry of Moduli Spaces and Representation Theory Book in PDF, ePub and Kindle
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.
| 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.
| Author | : Shmuel Weinberger |
| Publisher | : Princeton University Press |
| Total Pages | : 204 |
| Release | : 2005 |
| Genre | : Computers |
| ISBN | : 9780691118895 |
Download Computers, Rigidity, and Moduli Book in PDF, ePub and Kindle
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.
| 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 | : 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 | : Eckart Viehweg |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 329 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642797458 |
Download Quasi-projective Moduli for Polarized Manifolds Book in PDF, ePub and Kindle
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.
| 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 | : 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.
