Extension Groups Of Tautological Sheaves On Hilbert Schemes Of Points On Surfaces

Author : Andreas Krug
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832532544
Total Pages : 130 pages
Book Rating : 4.43/5 ( download)

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Download or read book Extension Groups of Tautological Sheaves on Hilbert Schemes of Points on Surfaces written by Andreas Krug and published by Logos Verlag Berlin GmbH. This book was released on 2012 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis cohomological invariants of tensor products of tautological objects in the derived category of Hilbert schemes of points on surfaces are studied. The main tool is the Bridgeland-King-Reid-Haiman equivalence between the derived category of the Hilbert scheme and the equivariant derived category of the cartesian power of the surface. The work of Scala on this topic is further developed leading to a new description of the image of tensor products of tautological bundles under the BKRH equivalence. This description leads to formulas for the Euler characteristics of triple tensor products of tautological objects for arbitrary n and for arbitrary tensor products in the case n=2. Furthermore a formula for the extension groups between tautological objects is proven and the Yoneda product is described.

Author : Christian Nolde
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832544534
Total Pages : 88 pages
Book Rating : 4.39/5 ( download)

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Download or read book Global Regularity and Uniqueness of Solutions in a Surface Growth Model Using Rigorous A-Posteriori Methods written by Christian Nolde and published by Logos Verlag Berlin GmbH. This book was released on 2017-04-20 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of rigorous numerical methods to approach problems which can not be solved using standard methods (yet) has increased signifiantly in recent years. In this book, riogorous a-posteriori methods are used to study the time evolution of a surface growth model, given by a fourth order semi-linear parabolic partial differential equation, where standard methods fail to verify global uniqueness and smoothness of solutions. Based on an arbitrary numerical approximation, a-posteriori error-analysis is applied in order to prevent a blow up analytically. This is a method that in a similar way also applies to the three dimensional Navier-Stokes equations. The main idea consists of energy-estimates for the error between solution and approximation that yields a scalar differential equation controlling the norm of the error with coefficients depending solely on the numerical data. This allows the solution of the differential equation to be bounded using only numerical data. A key technical tool is a rigorous eigenvalue bound for the nonlinear operator linearized around the numerical approximation. The presented method succeeds to show global uniqueness for relatively large initial conditions, which is demonstrated in many numerical examples.

Author : Martin Jesenko
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 383254478X
Total Pages : 145 pages
Book Rating : 4.82/5 ( download)

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Download or read book Commutability of Gamma-limits in problems with multiple scales written by Martin Jesenko and published by Logos Verlag Berlin GmbH. This book was released on 2017-05-15 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the calculus of variations, the goal is to explore extrema of a given integral functional. From origins of the problem, it might be expected that the functional can be adequately simplified by neglecting some small quantities. A way to rigorously justify such an approximation is the Γ-convergence that ensures convergence of corresponding (global) extrema. The main motivation of this work is to investigate properties of doubly indexed integral functionals that Γ-converge for one index fixed. In other words, for two possible approximations we would like to determine whether we may perform them consecutively and if they commute. Our examples are taken from material science with homogenization being one of these two processes. In the first part we are considering a setting related to the elastic regime. However, our assumptions are fairly general and allow for applications in different areas. The second part is devoted to problems in the Hencky plasticity. They are considerably different due to special growth properties of the density.

Author : Daniel Huybrechts
Publisher : Cambridge University Press
ISBN 13 : 1139485822
Total Pages : 345 pages
Book Rating : 4.21/5 ( download)

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Download or read book The Geometry of Moduli Spaces of Sheaves written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2010-05-27 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Hiraku Nakajima
Publisher : American Mathematical Soc.
ISBN 13 : 0821819569
Total Pages : 146 pages
Book Rating : 4.62/5 ( download)

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Download or read book Lectures on Hilbert Schemes of Points on Surfaces written by Hiraku Nakajima and published by American Mathematical Soc.. This book was released on 1999 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has been realized that Hilbert schemes originally studied in algebraic geometry are closely related to several branches of mathematics, such as singularities, symplectic geometry, representation theory - even theoretical physics. This book reflects this feature of Hilbert schemes.

Author : David Eisenbud
Publisher : Springer Science & Business Media
ISBN 13 : 0387226397
Total Pages : 265 pages
Book Rating : 4.92/5 ( download)

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Download or read book The Geometry of Schemes written by David Eisenbud and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.

Author : Eckart Viehweg
Publisher : Springer Science & Business Media
ISBN 13 : 3642797458
Total Pages : 329 pages
Book Rating : 4.53/5 ( download)

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Download or read book Quasi-projective Moduli for Polarized Manifolds written by Eckart Viehweg and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Daniel Huybrechts
Publisher : Cambridge University Press
ISBN 13 : 1316797252
Total Pages : 499 pages
Book Rating : 4.59/5 ( download)

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Download or read book Lectures on K3 Surfaces written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2016-09-26 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi–Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs, such as the proof of the Tate conjecture for K3 surfaces and structural results on Chow groups. Powerful general techniques are introduced to study the many facets of K3 surfaces, including arithmetic, homological, and differential geometric aspects. In this context, the book covers Hodge structures, moduli spaces, periods, derived categories, birational techniques, Chow rings, and deformation theory. Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin–Tate, are discussed in general and for K3 surfaces in particular, and each chapter ends with questions and open problems. Based on lectures at the advanced graduate level, this book is suitable for courses and as a reference for researchers.

Author :
Publisher :
ISBN 13 :
Total Pages : 866 pages
Book Rating : 4.79/5 ( download)

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Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Barbara Fantechi
Publisher : American Mathematical Soc.
ISBN 13 : 0821842455
Total Pages : 354 pages
Book Rating : 4.54/5 ( download)

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Download or read book Fundamental Algebraic Geometry written by Barbara Fantechi and published by American Mathematical Soc.. This book was released on 2005 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an outline of Alexander Grothendieck's theories. This book discusses four main themes - descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. It is suitable for those working in algebraic geometry.