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Calabi-Yau Manifolds and Related Geometries
 
 
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Calabi-Yau Manifolds and Related Geometries [Paperback]

Mark Gross (Author), Daniel Huybrechts (Author), Dominic Joyce (Author), Geir Ellingsrud (Editor), Loren Olson (Editor), Kristian Ranestad (Editor), Stein A. Stromme (Editor)

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Book Description

3540440593 978-3540440598 January 17, 2003 1
This is an introduction to a very active field of research, on the boundary between mathematics and physics. It is aimed at graduate students and researchers in geometry and string theory. Proofs or sketches are given for many important results. From the reviews: "An excellent introduction to current research in the geometry of Calabi-Yau manifolds, hyper-Kähler manifolds, exceptional holonomy and mirror symmetry....This is an excellent and useful book." --MATHEMATICAL REVIEWS

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Editorial Reviews

Review

From the reviews: "Summer schools in Nordfjordeid, Norway, have been organized regularly since 1996. Topics vary each year but there are always three series of lectures by invited experts with evening exercises. […] The themes of all three contributions are interrelated and together they give a nice introduction into a very interesting field of research on the border between mathematics and physics. l would like to strongly recommend the book to anybody interested in the topic." (jbu) European Mathematical Society Newsletter, Sept. 2004, p. 44 "[...] This book is an excellent introduction to current research in the geometry of Calabi-Yau manifolds, hyper-Kähler manifolds, exceptional holonomy and mirror symmetry. [...] This is an excellent and useful book. The different chapters mostly fit together reasonably well [...]. It will be popular with anyone trying to learn about Kähler manifolds with c1=0 and mirror symmetry." Richard P. Thomas, Mathematical Reviews, Clippings from Issue 2004c "Summer schools in Nordfjordeid, Norway, have been organized regularly since 1996. … The school held in June 2001 was devoted to recent interaction between differential and algebraic geometry. The book consists of notes written by lecturers of the corresponding three series of lectures. … they give a nice introduction into a very interesting field of research on the border between mathematics and physics. I would like to strongly recommend the book to anybody interested in the topic." (EMS, September, 2004) "This book is an excellent introduction to current research in the geometry of Calabi-Yau manifolds, hyper-Kähler manifolds, exceptional holonomy and mirror symmetry. … the choice of topics is a sensible one. … This is an excellent and useful book. … It will be popular with anyone trying to learn about Kähler manifolds with c1 = 0 and mirror symmetry." (Richard P. Thomas, Mathematical Reviews, 2004 c)

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Inside This Book (learn more)
First Sentence:
We begin by giving some background from differential and Riemannian geometry, principally to establish notation, and move on to discuss connections on vector bundles, parallel transport, and the definition of holonomy groups. Read the first page
Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
holomorphic symplectic manifold, large complex structure limit point, corresponding calibrated submanifolds, monodromy diffeomorphism, complex moduli space, monodromy weight filtration, isomorphic periods, exceptional holonomy groups, nilpotent orbit theorem, holomorphic symplectic structure, mirror symmetry conjecture, special holonomy, deformation equivalence, singular fibres, trivial canonical bundle, stable sheaves, birational map, twistor space, calibrated geometry, quartic hypersurface, birational correspondence, general fibre, exceptional locus, monodromy transformation, symplectic manifolds
Key Phrases - Capitalized Phrases (CAPs): (learn more)
Manifolds Let, Geometric Measure Theory
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