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Modular Calabi-Yau Threefolds

2005 Mathematics
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Release : 2005
Genre : Mathematics
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Book Rating : 08X/5 ( reviews)

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Book Synopsis Modular Calabi-Yau Threefolds by : Christian Meyer

Download or read book Modular Calabi-Yau Threefolds written by Christian Meyer. This book was released on 2005. Available in PDF, EPUB and Kindle. Book excerpt: "The main subject of this book is the connection between Calabi-Yau threefolds and modular forms. The book presents the general theory and brings together the known results. It studies hundreds of new examples of rigid and non-rigid modular Calabi-Yau threefolds and correspondences between them. Conjectures about the possible levels of modular forms connected with Calabi-Yau threefolds are presented. Tables of newforms of weight four and large levels are compiled and included in the appendix."--Jaquette.

Modular Calabi-Yau Threefolds in String Compactifications

2020
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Release : 2020
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Book Synopsis Modular Calabi-Yau Threefolds in String Compactifications by : Mohamed Abdulwahid Jama Elmi

Download or read book Modular Calabi-Yau Threefolds in String Compactifications written by Mohamed Abdulwahid Jama Elmi. This book was released on 2020. Available in PDF, EPUB and Kindle. Book excerpt:

A Dictionary of Modular Threefolds

2005
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Release : 2005
Genre :
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Book Synopsis A Dictionary of Modular Threefolds by :

Download or read book A Dictionary of Modular Threefolds written by . This book was released on 2005. Available in PDF, EPUB and Kindle. Book excerpt: The thesis deals with the modularity conjecture for three-dimensional Calabi-Yau varieties. This is a generalization of the work of A. Wiles and others on modularity of elliptic curves. Modularity connects the number of points on varieties with coefficients of certain modular forms. In chapter 1 we collect the basics on arithmetic on Calabi-Yau manifolds, including general modularity results and strategies for modularity proofs. In chapters 2, 3, 4 and 5 we investigate examples of modular Calabi-Yau threefolds, including all examples occurring in the literature and many new ones. Double octics, i.e. Double coverings of projective 3-space branched along an octic surface, are studied in detail. In chapter 6 we deal with examples connected with the same modular forms. According to the Tate conjecture there should be correspondences between them. Many correspondences are constructed explicitly. We finish by formulating conjectures on the occurring newforms, especially their levels. In the appendices we compile tables of coefficients of weight 2 and weight 4 newforms and many examples of double octics.

A Modular Non-rigid Calabi-Yau Threefold

2004 Calabi-Yau manifolds
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Release : 2004
Genre : Calabi-Yau manifolds
Kind : eBook
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Book Synopsis A Modular Non-rigid Calabi-Yau Threefold by : Edward Dole Lee

Download or read book A Modular Non-rigid Calabi-Yau Threefold written by Edward Dole Lee. This book was released on 2004. Available in PDF, EPUB and Kindle. Book excerpt:

Calabi-Yau Varieties and Mirror Symmetry

2003 Mathematics
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Release : 2003
Genre : Mathematics
Kind : eBook
Book Rating : 553/5 ( reviews)

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Book Synopsis Calabi-Yau Varieties and Mirror Symmetry by : Noriko Yui

Download or read book Calabi-Yau Varieties and Mirror Symmetry written by Noriko Yui. This book was released on 2003. Available in PDF, EPUB and Kindle. Book excerpt: The idea of mirror symmetry originated in physics, but in recent years, the field of mirror symmetry has exploded onto the mathematical scene. It has inspired many new developments in algebraic and arithmetic geometry, toric geometry, the theory of Riemann surfaces, and infinite-dimensional Lie algebras among others. The developments in physics stimulated the interest of mathematicians in Calabi-Yau varieties. This led to the realization that the time is ripe for mathematicians, armed with many concrete examples and alerted by the mirror symmetry phenomenon, to focus on Calabi-Yau varieties and to test for these special varieties some of the great outstanding conjectures, e.g., the modularity conjecture for Calabi-Yau threefolds defined over the rationals, the Bloch-Beilinson conjectures, regulator maps of higher algebraic cycles, Picard-Fuchs differential equations, GKZ hypergeometric systems, and others. The articles in this volume report on current developments. The papers are divided roughly into two categories: geometric methods and arithmetic methods. One of the significant outcomes of the workshop is that we are finally beginning to understand the mirror symmetry phenomenon from the arithmetic point of view, namely, in terms of zeta-functions and L-series of mirror pairs of Calabi-Yau threefolds. The book is suitable for researchers interested in mirror symmetry and string theory.

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