Betti Numbers Of The Moduli Space Of Rank 3 Parabolic Higgs Bundles
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Betti Numbers Of The Moduli Space Of Rank 3 Parabolic Higgs Bundles
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Author : Oscar García-Prada
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Betti Numbers Of The Moduli Space Of Rank 3 Parabolic Higgs Bundles written by Oscar García-Prada and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Parabolic Higgs bundles on a Riemann surface are of interest for many reasons, one of them being their importance in the study of representations of the fundamental group of the punctured surface in the complex general linear group. in this paper the authors calculate the Betti numbers of the moduli space of rank 3 parabolic Higgs bundles with fixed and non-fixed determinant, using Morse theory. A key point is that certain critical submanifolds of the Morse function can be identified with moduli spaces of parabolic triples. These moduli spaces come in families depending on a real parameter and the authors carry out a careful analysis of them by studying their variation with this parameter. Thus the authors obtain in particular information about the topology of the moduli spaces of parabolic triples for the value of the parameter relevant to the study of parabolic Higgs bundles. The remaining critical submanifolds are also described: one of them is the moduli space of parabolic bundles, while the rem
Betti Numbers Of The Moduli Space Of Rank 3 Parabolic Higgs Bundles
DOWNLOAD
Author : Oscar García-Prada
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Betti Numbers Of The Moduli Space Of Rank 3 Parabolic Higgs Bundles written by Oscar García-Prada and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Parabolic Higgs bundles on a Riemann surface are of interest for many reasons, one of them being their importance in the study of representations of the fundamental group of the punctured surface in the complex general linear group. In this paper the authors calculate the Betti numbers of the moduli space of rank 3 parabolic Higgs bundles with fixed and non-fixed determinant,
The Many Facets Of Geometry
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Author : Oscar Garcia-Prada
language : en
Publisher: OUP Oxford
Release Date : 2010-07-01
The Many Facets Of Geometry written by Oscar Garcia-Prada and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-01 with Mathematics categories.
Few people have proved more influential in the field of differential and algebraic geometry, and in showing how this links with mathematical physics, than Nigel Hitchin. Oxford University's Savilian Professor of Geometry has made fundamental contributions in areas as diverse as: spin geometry, instanton and monopole equations, twistor theory, symplectic geometry of moduli spaces, integrables systems, Higgs bundles, Einstein metrics, hyperkähler geometry, Frobenius manifolds, Painlevé equations, special Lagrangian geometry and mirror symmetry, theory of grebes, and many more. He was previously Rouse Ball Professor of Mathematics at Cambridge University, as well as Professor of Mathematics at the University of Warwick, is a Fellow of the Royal Society and has been the President of the London Mathematical Society. The chapters in this fascinating volume, written by some of the greats in their fields (including four Fields Medalists), show how Hitchin's ideas have impacted on a wide variety of subjects. The book grew out of the Geometry Conference in Honour of Nigel Hitchin, held in Madrid, with some additional contributions, and should be required reading for anyone seeking insights into the overlap between geometry and physics.
Vector Bundles And Complex Geometry
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Author : Oscar García-Prada
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Vector Bundles And Complex Geometry written by Oscar García-Prada and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
This volume contains a collection of papers from the Conference on Vector Bundles held at Miraflores de la Sierra, Madrid, Spain on June 16-20, 2008, which honored S. Ramanan on his 70th birthday. The main areas covered in this volume are vector bundles, parabolic bundles, abelian varieties, Hilbert schemes, contact structures, index theory, Hodge theory, and geometric invariant theory. Professor Ramanan has made important contributions in all of these areas.
Moduli Spaces
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Author : Leticia Brambila
language : en
Publisher: Cambridge University Press
Release Date : 2014-03-13
Moduli Spaces written by Leticia Brambila and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-13 with Mathematics categories.
A graduate-level introduction to some of the important contemporary ideas and problems in the theory of moduli spaces.
Rank One Higgs Bundles And Representations Of Fundamental Groups Of Riemann Surfaces
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Author : William Mark Goldman
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Rank One Higgs Bundles And Representations Of Fundamental Groups Of Riemann Surfaces written by William Mark Goldman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This expository article details the theory of rank one Higgs bundles over a closed Riemann surface $X$ and their relation to representations of the fundamental group of $X$. The authors construct an equivalence between the deformation theories of flat connections and Higgs pairs. This provides an identification of moduli spaces arising in different contexts. The moduli spaces are real Lie groups. From each context arises a complex structure, and the different complex structures define a hyperkähler structure. The twistor space, real forms, and various group actions are computed explicitly in terms of the Jacobian of $X$. The authors describe the moduli spaces and their geometry in terms of the Riemann period matrix of $X$.
Calabi Yau Varieties Arithmetic Geometry And Physics
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Author : Radu Laza
language : en
Publisher: Springer
Release Date : 2015-08-27
Calabi Yau Varieties Arithmetic Geometry And Physics written by Radu Laza and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-27 with Mathematics categories.
This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi–Yau varieties and string theory. With its coverage of the various perspectives of a wide area of topics such as Hodge theory, Gross–Siebert program, moduli problems, toric approach, and arithmetic aspects, the book gives a comprehensive overview of the current streams of mathematical research in the area. The contributions in this book are based on lectures that took place during workshops with the following thematic titles: “Modular Forms Around String Theory,” “Enumerative Geometry and Calabi–Yau Varieties,” “Physics Around Mirror Symmetry,” “Hodge Theory in String Theory.” The book is ideal for graduate students and researchers learning about Calabi–Yau varieties as well as physics students and string theorists who wish to learn the mathematics behind these varieties.
Geometric Invariant Theory And Decorated Principal Bundles
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Author : Alexander H. W. Schmitt
language : en
Publisher: European Mathematical Society
Release Date : 2008
Geometric Invariant Theory And Decorated Principal Bundles written by Alexander H. W. Schmitt and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The book starts with an introduction to Geometric Invariant Theory (GIT). The fundamental results of Hilbert and Mumford are exposed as well as more recent topics such as the instability flag, the finiteness of the number of quotients, and the variation of quotients. In the second part, GIT is applied to solve the classification problem of decorated principal bundles on a compact Riemann surface. The solution is a quasi-projective moduli scheme which parameterizes those objects that satisfy a semistability condition originating from gauge theory. The moduli space is equipped with a generalized Hitchin map. Via the universal Kobayashi-Hitchin correspondence, these moduli spaces are related to moduli spaces of solutions of certain vortex type equations. Potential applications include the study of representation spaces of the fundamental group of compact Riemann surfaces. The book concludes with a brief discussion of generalizations of these findings to higher dimensional base varieties, positive characteristic, and parabolic bundles. The text is fairly self-contained (e.g., the necessary background from the theory of principal bundles is included) and features numerous examples and exercises. It addresses students and researchers with a working knowledge of elementary algebraic geometry.
Toroidal Dehn Fillings On Hyperbolic 3 Manifolds
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Author : Cameron Gordon
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Toroidal Dehn Fillings On Hyperbolic 3 Manifolds written by Cameron Gordon and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The authors determine all hyperbolic $3$-manifolds $M$ admitting two toroidal Dehn fillings at distance $4$ or $5$. They show that if $M$ is a hyperbolic $3$-manifold with a torus boundary component $T 0$, and $r,s$ are two slopes on $T 0$ with $\Delta(r,s) = 4$ or $5$ such that $M(r)$ and $M(s)$ both contain an essential torus, then $M$ is either one of $14$ specific manifolds $M i$, or obtained from $M 1, M 2, M 3$ or $M {14}$ by attaching a solid torus to $\partial M i - T 0$.All the manifolds $M i$ are hyperbolic, and the authors show that only the first three can be embedded into $S3$. As a consequence, this leads to a complete classification of all hyperbolic knots in $S3$ admitting two toroidal surgeries with distance at least $4$.
Toroidalization Of Dominant Morphisms Of 3 Folds
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Author : Steven Dale Cutkosky
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Toroidalization Of Dominant Morphisms Of 3 Folds written by Steven Dale Cutkosky and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This book contains a proof that a dominant morphism from a 3-fold $X$ to a variety $Y$ can be made toroidal by blowing up in the target and domain. We give applications to factorization of birational morphisms of 3-folds.