FURTHER READING
- David A. Cox and Sheldon Katz, Mirror Symmetry and Algebraic Geometry, American Mathematical Society, Providence, RI, 1991. The standard graduate-level text on mathematical mirror symmetry.
- Charles F. Doran and Andrey Novoseltsev, Closed form expressions for Hodge numbers of complete intersection Calabi-Yau threefolds in toric varieties, Contemporary Mathematics 527 (2010) 1–14. http://dx.doi.org/10.1090/conm/527/10398. Explicit equations for Hodge numbers of Calabi-Yau threefolds in terms of polytope data.
- Brian Greene, The Elegant Universe, Vintage Books, New York, 2003. A popular introduction to string theory by one of the field's pioneers. Chapter 10 describes physicists' discovery of mirror symmetry.
- Andrew J. Hanson and Jeff Bryant, Calabi-Yau space, Wolfram Demonstrations Project, http://demonstrations.wolfram.com/CalabiYauSpace/. Mathematica code for visualizing a Calabi-Yau threefold.
- Sheldon Katz, Enumerative Geometry and String Theory, American Mathematical Society, Providence, RI, 2006. This book, based on lectures for advanced undergraduate students at the Park City Mathematics Institute, describes another surprising connection between string theory and mathematics: We can use ideas from string theory to count subspaces of geometric spaces, such as the number of curves on a Calabi-Yau threefold.
- Maximilian Kreuzer and Harald Skarke, Calabi-Yau data, http://hep.itp.tuwien.ac.at/~kreuzer/CY/. Data on the classification of reflexive polytopes.
- Benjamin Nill, Gorenstein toric Fano varieties, preprint, http://arxiv.org/abs/math/0405448 (May 24, 2004). A discussion of Fano and reflexive polytopes, and their relationship to geometric spaces called toric varieties. A version of this paper was published in Manuscripta Mathematica 116 (2005) 183–210, but only the preprint gives the classification of reflexive polygons.
- Bjorn Poonen and Fernando Rodriguez-Villegas, Lattice polygons and the number 12, Amer. Math. Monthly 107 (2000) 238–250. http://dx.doi.org/10.2307/2589316. Why is the sum of the lattice points on the boundary of a mirror pair of polygons always 12? Proofs involving combinatorics and number theory.
- Shing-Tung Yau and Steve Nadis, The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions, Basic Books, New York, 2010. Yau won the Fields Medal for his work on Calabi-Yau manifolds. He teamed up with a science journalist to write this book, aimed at a general audience, on the geometry of Calabi-Yau manifolds and the implications for string theory.