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

  • Dan Abramovich
  • Marcos Mariño
  • Michael Thaddeus
  • Ravi Vakil
  • Kai Behrend
  • Marco Manetti

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

Table of contents

  1. Front Matter
    Pages I-X
  2. M. Mariño
    Pages 49-104
  3. M. Thaddeus
    Pages 105-141
  4. Back Matter
    Pages 199-210

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.


Algebra Cohomology Gromov-Witten invariants enumerative geometry moduli space orbifolds quantum cohomology string theory

Authors and affiliations

  • Dan Abramovich
    • 1
  • Marcos Mariño
    • 2
  • Michael Thaddeus
    • 3
  • Ravi Vakil
    • 4
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA
  2. 2.Department of Physics Theory DivisionUniversity of GenevaGenevaSwitzerland
  3. 3.Department of MathematicsColumbia UniversityNew YorkUSA
  4. 4.Department of MathematicsStanford UniversityStanfordUSA

Editors and affiliations

  • Kai Behrend
    • 1
  • Marco Manetti
    • 2
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Department of Mathematics “Guido Castelnuovo”University of Rome “La Sapienza”Italy

Bibliographic information

  • DOI
  • Copyright Information Springer Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-79813-2
  • Online ISBN 978-3-540-79814-9
  • Series Print ISSN 0075-8434
  • Buy this book on publisher's site