By Tadao Oda

The speculation of toric types (also known as torus embeddings) describes a desirable interaction among algebraic geometry and the geometry of convex figures in actual affine areas. This publication is a unified up to date survey of a number of the effects and fascinating functions discovered considering that toric types have been brought within the early 1970's. it's an up-to-date and corrected English variation of the author's publication in jap released via Kinokuniya, Tokyo in 1985. Toric forms are the following handled as advanced analytic areas. with out assuming a lot past wisdom of algebraic geometry, the writer indicates how simple convex figures provide upward push to attention-grabbing complicated analytic areas. simply visualized convex geometry is then used to explain algebraic geometry for those areas, similar to line bundles, projectivity, automorphism teams, birational adjustments, differential types and Mori's thought. for this reason this booklet may possibly function an obtainable advent to present algebraic geometry. Conversely, the algebraic geometry of toric kinds provides 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 accrued jointly within the appendix.

**Read 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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