By Tadao Oda
The speculation of toric forms (also known as torus embeddings) describes a desirable interaction among algebraic geometry and the geometry of convex figures in genuine affine areas. This publication is a unified updated survey of a number of the effects and fascinating functions discovered given that toric kinds have been brought within the early 1970's. it really is an up-to-date and corrected English version of the author's booklet in jap released by way of Kinokuniya, Tokyo in 1985. Toric forms are the following handled as complicated analytic areas. with out assuming a lot previous wisdom of algebraic geometry, the writer indicates how effortless convex figures supply upward push to attention-grabbing advanced analytic areas. simply visualized convex geometry is then used to explain algebraic geometry for those areas, akin to line bundles, projectivity, automorphism teams, birational ameliorations, differential types and Mori's thought. accordingly this booklet may perhaps function an available creation to present algebraic geometry. Conversely, the algebraic geometry of toric forms supplies new perception into persevered fractions in addition to their higher-dimensional analogues, the isoperimetric challenge and different questions about convex our bodies. correct effects on convex geometry are amassed jointly within the appendix.
Read Online or Download Convex Bodies and Algebraic Geometry: An Introduction to the Theory of Toric Varieties (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics) PDF
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