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Enumerative Invariants in Algebraic Geometry and String Theory

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 6-11, 2005

  • Book
  • © 2008

Overview

Authors:
  1. Dan Abramovich

    1. Department of Mathematics, Brown University, Providence, USA

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  2. Marcos Mariño

    1. Department of Physics Theory Division, University of Geneva, Geneva, Switzerland

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  3. Michael Thaddeus

    1. Department of Mathematics, Columbia University, New York, USA

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  4. Ravi Vakil

    1. Department of Mathematics, Stanford University, Stanford, USA

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Editors:
  1. Kai Behrend

    1. Department of Mathematics, University of British Columbia, Vancouver, Canada

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  2. Marco Manetti

    1. Department of Mathematics “Guido Castelnuovo”, University of Rome “La Sapienza”, Italy

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1947)

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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Table of contents (4 chapters)

  1. Front Matter

    Pages I-X
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  2. Lectures on Gromov–Witten Invariants of Orbifolds

    • D. Abramovich
    Pages 1-48

  3. Lectures on the Topological Vertex

    • M. Mariño
    Pages 49-104

  4. Floer Cohomology with Gerbes

    • M. Thaddeus
    Pages 105-141

  5. The Moduli Space of Curves and Gromov–Witten Theory

    • R. Vakil
    Pages 143-198

  6. Back Matter

    Pages 199-210
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Keywords

About this book

Starting in the middle of the 80s, there has been a growing and fruitful interaction between algebraic geometry and certain areas of theoretical high-energy physics, especially the various versions of string theory. Physical heuristics have provided inspiration for new mathematical definitions (such as that of Gromov-Witten invariants) leading in turn to the solution of problems in enumerative geometry. Conversely, the availability of mathematically rigorous definitions and theorems has benefited the physics research by providing the required evidence in fields where experimental testing seems problematic. The aim of this volume, a result of the CIME Summer School held in Cetraro, Italy, in 2005, is to cover part of the most recent and interesting findings in this subject.

Authors, Editors and Affiliations

  • Department of Mathematics, University of British Columbia, Vancouver, Canada

    Kai Behrend

  • Department of Mathematics “Guido Castelnuovo”, University of Rome “La Sapienza”, Italy

    Marco Manetti

  • Department of Mathematics, Brown University, Providence, USA

    Dan Abramovich

  • Department of Physics Theory Division, University of Geneva, Geneva, Switzerland

    Marcos Mariño

  • Department of Mathematics, Columbia University, New York, USA

    Michael Thaddeus

  • Department of Mathematics, Stanford University, Stanford, USA

    Ravi Vakil

About the editors

Dan Abramovich is a Professor of Mathematics at Brown University, working on Birational Geometry and Moduli Spaces.

Marco Manetti is a Professor of Mathematics at Sapienza University of Rome, working on Algebraic Geometry and Deformation Theory.

Bibliographic Information

  • Book Title: Enumerative Invariants in Algebraic Geometry and String Theory

  • Book Subtitle: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 6-11, 2005

  • Authors: Dan Abramovich, Marcos Mariño, Michael Thaddeus, Ravi Vakil

  • Editors: Kai Behrend, Marco Manetti

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-540-79814-9

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2008

  • Softcover ISBN: 978-3-540-79813-2Published: 22 August 2008

  • eBook ISBN: 978-3-540-79814-9Published: 15 August 2008

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 210

  • Number of Illustrations: 30 b/w illustrations

  • Topics: Algebra, Algebraic Geometry, Differential Geometry, Quantum Physics

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