• Corpus ID: 9746750

Lectures on complex geometry, Calabi-Yau manifolds and toric geometry

@article{Bouchard2007LecturesOC,
  title={Lectures on complex geometry, Calabi-Yau manifolds and toric geometry},
  author={Vincent Bouchard},
  journal={arXiv: High Energy Physics - Theory},
  year={2007}
}
  • V. Bouchard
  • Published 8 February 2007
  • Mathematics
  • arXiv: High Energy Physics - Theory
These are introductory lecture notes on complex geometry, Calabi-Yau manifolds and toric geometry. We first define basic concepts of complex and Kahler geometry. We then proceed with an analysis of various definitions of Calabi-Yau manifolds. The last section provides a short introduction to toric geometry, aimed at constructing Calabi-Yau manifolds in two different ways: as hypersurfaces in toric varieties and as local toric Calabi-Yau threefolds. These lecture notes supplement a mini-course… 

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References

SHOWING 1-10 OF 29 REFERENCES

Compact Manifolds with Special Holonomy

The book starts with a thorough introduction to connections and holonomy groups, and to Riemannian, complex and Kahler geometry. Then the Calabi conjecture is proved and used to deduce the existence

String Theory on Calabi-Yau Manifolds

These lectures are devoted to introducing some of the basic features of quantum geometry that have been emerging from compactified string theory over the last couple of years. The developments

Toric Geometry and String Theory

In this thesis we probe various interactions between toric geometry and string theory. First, the notion of a top was introduced by Candelas and Font as a useful tool to investigate string dualities.

Calabi‐Yau Manifolds: A Bestiary for Physicists

Calabi-Yau spaces are complex spaces with a vanishing first Chern class, or equivalently, with trivial canonical bundle (canonical class). They are used to construct possibly realistic (super)string

String dualities and toric geometry: an introduction

On The Ricci Curvature of a Compact Kahler Manifold and the Complex Monge-Ampere Equation, I*

Therefore a necessary condition for a (1,l) form ( G I a ' r r ) I,,, Rlr dz' A d? to be the Ricci form of some Kahler metric is that it must be closed and its cohomology class must represent the

Introduction to toric varieties

The course given during the School and Workshop “The Geometry and Topology of Singularities”, 8-26 January 2007, Cuernavaca, Mexico is based on a previous course given during the 23o Coloquio

Principles of Algebraic Geometry

A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications

Chern-Simons theory and topological strings

A review of the relation between Chern-Simons gauge theory and topological string theory on noncompact Calabi-Yau spaces is given. This relation has made it possible to give an exact solution of

Affine Kac-Moody algebras, CHL strings and the classification of tops

Candelas and Font introduced the notion of a `top' as half of a three dimensional reflexive polytope and noticed that Dynkin diagrams of enhanced gauge groups in string theory can be read off from