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Introduction to Toric Varieties. (AM-131)

Introduction to Toric Varieties. (AM-131)

  • Author: William Fulton
  • Publisher: Princeton University Press
  • ISBN: 1400882524
  • Category: Mathematics
  • Page: 180
  • View: 8684
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Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic geometry notions such as singularities, birational maps, cycles, homology, intersection theory, and Riemann-Roch translate into simple facts about polytopes, toric varieties provide a marvelous source of examples in algebraic geometry. In the other direction, general facts from algebraic geometry have implications for such polytopes, such as to the problem of the number of lattice points they contain. In spite of the fact that toric varieties are very special in the spectrum of all algebraic varieties, they provide a remarkably useful testing ground for general theories. The aim of this mini-course is to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications. The text concludes with Stanley's theorem characterizing the numbers of simplicies in each dimension in a convex simplicial polytope. Although some general theorems are quoted without proof, the concrete interpretations via simplicial geometry should make the text accessible to beginners in algebraic geometry.

Das Kontinuum diskret berechnen

Das Kontinuum diskret berechnen

  • Author: Matthias Beck,Sinai Robins
  • Publisher: Springer-Verlag
  • ISBN: 3540795960
  • Category: Mathematics
  • Page: 242
  • View: 2183
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Das Gebiet des „Zählens von Gitterpunkten in Polytopen", auch Ehrhart-Theorie genannt, bietet verschiedene Verbindungen: zu elementarer endlicher Fourier-Analysis, zum Münzenproblem von Frobenius, zu Raumwinkeln, magischen Quadraten, Dedekind-Summen und vielem mehr. Dies nutzen die Autoren und knüpfen einen roten Faden, der so die grundlegenden Ideen aus diskreter Geometrie, Kombinatorik und Zahlentheorie verbindet. 250 Aufgaben und offene Probleme sowie der ansprechende Stil der Autoren laden zum Mitdenken ein.

Strings, Gauge Fields, and the Geometry Behind

Strings, Gauge Fields, and the Geometry Behind

The Legacy of Maximilian Kreuzer

  • Author: Anton Rebhan,Ludmil Katzarkov,Johanna Knapp,Radoslav Rashkov,Emanuel Scheidegger
  • Publisher: World Scientific
  • ISBN: 9814412562
  • Category: Mathematics
  • Page: 568
  • View: 2691
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This book contains exclusively invited contributions from collaborators of Maximilian Kreuzer, giving accounts of his scientific legacy and original articles from renowned theoretical physicists and mathematicians, including Victor Batyrev, Philip Candelas, Michael Douglas, Alexei Morozov, Joseph Polchinski, Peter van Nieuwenhuizen, and Peter West. Besides a collection of review and research articles from high-profile researchers in string theory and related fields of mathematics (in particular, algebraic geometry) which discuss recent progress in the exploration of string theory vacua and corresponding mathematical developments, this book contains a pedagogical account of the important work of Brandt, Dragon, and Kreuzer on classification of anomalies in gauge theories. This highly cited work, which is also quoted in the textbook of Steven Weinberg on quantum field theory, has not yet been presented in full detail except in private lecture notes by Norbert Dragon. Similarly, the software package PALP (Package for Analyzing Lattice Polytopes with applications to toric geometry), which has been incorporated in the SAGE (Software for Algebra and Geometry Experimentation) project, has not yet been documented in full detail. This book contains a user manual for a new thoroughly revised version of PALP. By including these two very useful original contributions, researchers in quantum field theory, string theory, and mathematics will find added value in a pedagogical presentation of the classification of quantum gauge field anomalies, and the accompanying comprehensive manual and tutorial for the powerful software package PALP. Contents:Gauge Field Theory, Anomalies, and Supersymmetry:BRST Symmetry and Cohomology (N Dragon and F Brandt)Aspects of Supersymmetric BRST Cohomology (F Brandt)Character Expansion for HOMFLY Polynomials: Integrability and Difference Equations (A Mironov, A Morozov and A Morozov)Bicategories in Field Theories — An Invitation (T Nikolaus and C Schweigert)The Compactification of IIB Supergravity on S5 Revisited (P van Nieuwenhuizen)String Theory and Algebraic Geometry:Max Kreuzer's Contributions to the Study of Calabi–Yau Manifolds (P Candelas)Calabi–Yau Three-Folds: Poincaré Polynomials and Fractals (A Ashmore and Y-H He)Conifold Degenerations of Fano 3-Folds as Hypersurfaces in Toric Varieties (V Batyrev and M Kreuzer)Nonassociativity in String Theory (R Blumenhagen)Counting Points and Hilbert Series in String Theory (V Braun)Standard Models and Calabi–Yaus (R Donagi)The String Landscape and Low Energy Supersymmetry (M R Douglas)The Cardy–Cartan Modular Invariant (J Fuchs, C Schweigert and C Stigner)A Projection to the Pure Spinor Space (S Guttenberg)Mathieu Moonshine and Symmetries of K3 Sigma Models (S Hohenegger)Toric Deligne–Mumford Stacks and the Better Behaved Version of the GKZ Hypergeometric System (R P Horja)Fano Polytopes (A M Kasprzyk and B Nill)Dual Purpose Landscaping Tools: Small Extra Dimensions in AdS/CFT (J Polchinski and E Silverstein)Notes on the Relation Between Strings, Integrable Models and Gauge Theories (R C Rashkov)E11, Generalised Space-Time and IIA String Theory: The R ⊗ R Sector (A Rocén and P West)The Kreuzer Bi-Homomorphism (A N Schellekens)Emergent Spacetime and Black Hole Probes from Automorphic Forms (R Schimmrigk)How to Classify Reflexive Gorenstein Cones (H Skarke)PALP — A Package for Analyzing Lattice Polytopes:PALP — A User Manual (A P Braun, J Knapp, E Scheidegger, H Skarke and N-O Walliser) Readership: Graduate students and researchers in theoretical physics and mathematics. Keywords:String Theory;Gauge Theory;Algebraic Geometry;Calabi–Yau Manifolds;Toric Geometry;Lattice Polytopes;BRST Symmetry;Cohomology;Anomalies;SupersymmetryKey Features:Original research articles contributed by prominent theoretical physicists and mathematicians (Victor Batyrev, Ralph Blumenhagen, Ron Donagi, Michael Douglas, Jürgen Fuchs, Alexei Morozov, Joseph Polchinski, Bert Schellekens, Christoph Schweigert, Eva Silverstein, Peter van Nieuwenhuizen, and Peter West, among others)Previously unpublished lecture notes on the classification of quantum gauge field anomalies by Friedemann Brandt and Norbert DragonA comprehensive manual and tutorial for the powerful software package PALP that was developed originally by Kreuzer and Skarke in connection with the classification of reflexive polytopes. Together with the publication of this memorial volume an overhauled version 2.1 of PALP will be released in the public domain

Introduction to Stokes Structures

Introduction to Stokes Structures

  • Author: Claude Sabbah
  • Publisher: Springer
  • ISBN: 3642316956
  • Category: Mathematics
  • Page: 249
  • View: 9518
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This research monograph provides a geometric description of holonomic differential systems in one or more variables. Stokes matrices form the extended monodromy data for a linear differential equation of one complex variable near an irregular singular point. The present volume presents the approach in terms of Stokes filtrations. For linear differential equations on a Riemann surface, it also develops the related notion of a Stokes-perverse sheaf. This point of view is generalized to holonomic systems of linear differential equations in the complex domain, and a general Riemann-Hilbert correspondence is proved for vector bundles with meromorphic connections on a complex manifold. Applications to the distributions solutions to such systems are also discussed, and various operations on Stokes-filtered local systems are analyzed.

Arrangements, Local Systems and Singularities

Arrangements, Local Systems and Singularities

CIMPA Summer School, Galatasaray University, Istanbul, 2007

  • Author: Fouad El Zein,Alexander I. Suciu,Meral Tosun,Muhammed Uludag,Sergey Yuzvinsky
  • Publisher: Springer Science & Business Media
  • ISBN: 9783034602099
  • Category: Mathematics
  • Page: 305
  • View: 9706
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This volume comprises the Lecture Notes of the CIMPA/TUBITAK Summer School Arrangements, Local systems and Singularities held at Galatasaray University, Istanbul during June 2007. The volume is intended for a large audience in pure mathematics, including researchers and graduate students working in algebraic geometry, singularity theory, topology and related fields. The reader will find a variety of open problems involving arrangements, local systems and singularities proposed by the lecturers at the end of the school.

Mathematisches Institut Georg-august-universität Göttingen, Seminars Summer 2003/2004

Mathematisches Institut Georg-august-universität Göttingen, Seminars Summer 2003/2004

  • Author: Yuri Tschinkel
  • Publisher: Universitätsverlag Göttingen
  • ISBN: 3930457512
  • Category: Mathematics
  • Page: 229
  • View: 6856
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Syzygies of toric varieties

Syzygies of toric varieties

  • Author: Milena S. Hering
  • Publisher: N.A
  • ISBN: N.A
  • Category:
  • Page: N.A
  • View: 8599
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Geometry of toric varieties

Geometry of toric varieties

  • Author: Laurent Bonavero,Michel Brion
  • Publisher: N.A
  • ISBN: N.A
  • Category: Algebraic varieties
  • Page: 272
  • View: 1188
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This volume gathers texts originated in the summer school "Geometry of Toric Varieties" (Grenoble, June 19-July 7, 2000). These are expanded versions of lectures delivered during the second and third weeks of the school, the first week having been devoted to introductory lectures. The paper by D. Cox is an overview of recent work in toric varieties and its applications, putting into perspective the other contributions of the présent volume. Ce volume rassemble des textes issus de l'école d'été " Géométrie des variétés toriques " (Grenoble, 19 juin - 7 juillet 2000). Ils reprennent, sous une forme plus détaillée, des cours et des exposés de séminaire des deuxième et troisième semaines de l'école, la première semaine ayant été consacrée à des cours introductifs. On trouvera dans l'article de D. Cox un panorama des travaux récents en géométrie torique et de leurs applications, qui met en perspective les autres textes du présent volume.

Mathematical Research Letters

Mathematical Research Letters

MRL

  • Author: N.A
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematics
  • Page: N.A
  • View: 2608
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A Computational Theory of Laurent Polynomial Rings and Multidimensional FIR Systems

A Computational Theory of Laurent Polynomial Rings and Multidimensional FIR Systems

  • Author: Hyung-Ju Park
  • Publisher: N.A
  • ISBN: N.A
  • Category:
  • Page: 252
  • View: 1537
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Singularités franco-japonaises

Singularités franco-japonaises

  • Author: Centre national de rencontres mathématiques (France)
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematics
  • Page: 460
  • View: 1698
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Grobner basis methods for integer programming

Grobner basis methods for integer programming

  • Author: Rekha Rachel Thomas
  • Publisher: N.A
  • ISBN: N.A
  • Category:
  • Page: 314
  • View: 453
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Saitama Mathematical Journal

Saitama Mathematical Journal

  • Author: N.A
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematics
  • Page: N.A
  • View: 7693
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Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

  • Author: N.A
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematics
  • Page: N.A
  • View: 9314
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Proceedings of the International Mathematical Congress held ...

Proceedings of the International Mathematical Congress held ...

  • Author: N.A
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematics
  • Page: N.A
  • View: 6335
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Memorandum

Memorandum

  • Author: N.A
  • Publisher: N.A
  • ISBN: N.A
  • Category: Electrical engineering
  • Page: N.A
  • View: 7577
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Bulletin (new Series) of the American Mathematical Society

Bulletin (new Series) of the American Mathematical Society

  • Author: N.A
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematics
  • Page: N.A
  • View: 5226
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Journal of physics : A, Mathematical and general

Journal of physics : A, Mathematical and general

  • Author: N.A
  • Publisher: N.A
  • ISBN: N.A
  • Category:
  • Page: N.A
  • View: 4754
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Introduction to geometric invariant theory

Introduction to geometric invariant theory

  • Author: Igor V. Dolgachev
  • Publisher: N.A
  • ISBN: N.A
  • Category: Geometry, Algebraic
  • Page: 137
  • View: 4206
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