Introduction to Toric Varieties (Softcover)
Introduction to Toric Varieties (Softcover)
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This is volume 131 in Princeton University Press'sAnnals of Mathematics Studies .From the Preface: "Algebraic geometry has developed a great deal of machinery for studying higher dimensional nonsingular and singular varieties; for example, all sorts of cohomology theories, resolution of singularities, Hodge theory, intersection theory, Reimann-Roch theorems, and vanishing theorems. There has been real progress recently toward at least a rough classification of higher dimensional varieties, particularly by Mori and his school. For all this—and for anyone learning algebraic geometry—it is important to have a good source of examples."
The author wrote about the study of toric varieties, "...we believe it provides a good companion for an introduction to algebraic geometry (but certainly not a substitute for the study of curves, surfaces, and projective geometry. ...
"The goal of this mini-course is to develop the foundational material, with many examples, and then to concentrate on the topology, intersection theory, and Riemann-Roch problem on toric varieties."
Chapters
- Definitions and examples
- Singularities and compactness
- Orbits, topology, and line bundles
- Moment maps and the tangent bundle
- Intersection theory
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PUBLISHER: Princeton University Press
ISBN-13: 9780691000497
ISBN-10: 0691000492