Download E-books 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

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.

Show description

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

Best Algebraic Geometry books

The Many Facets of Geometry: A Tribute to Nigel Hitchin (Oxford Science Publications)

Few humans have proved extra influential within the box of differential and algebraic geometry, and in displaying how this hyperlinks with mathematical physics, than Nigel Hitchin. Oxford University's Savilian Professor of Geometry has made primary contributions in components as assorted as: spin geometry, instanton and monopole equations, twistor conception, symplectic geometry of moduli areas, integrables platforms, Higgs bundles, Einstein metrics, hyperkähler geometry, Frobenius manifolds, Painlevé equations, targeted Lagrangian geometry and replicate symmetry, thought of grebes, and lots of extra.

The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra (Graduate Texts in Mathematics)

First textbook-level account of easy examples and strategies during this quarter. compatible for self-study through a reader who is familiar with a bit commutative algebra and algebraic geometry already. David Eisenbud is a widely known mathematician and present president of the yank Mathematical Society, in addition to a profitable Springer writer.

Measure, Topology, and Fractal Geometry (Undergraduate Texts in Mathematics)

In accordance with a path given to gifted high-school scholars at Ohio collage in 1988, this publication is basically a sophisticated undergraduate textbook concerning the arithmetic of fractal geometry. It properly bridges the space among conventional books on topology/analysis and extra really good treatises on fractal geometry.

Higher-Dimensional Algebraic Geometry (Universitext)

The category idea of algebraic forms is the focal point of this e-book. This very lively zone of analysis remains to be constructing, yet an awesome volume of information has amassed over the last 20 years. The authors aim is to supply an simply obtainable advent to the topic. The e-book begins with preparatory and conventional definitions and effects, then strikes directly to speak about a variety of elements of the geometry of gentle projective forms with many rational curves, and finishes in taking the 1st steps in the direction of Moris minimum version application of class of algebraic kinds by way of proving the cone and contraction theorems.

Additional info for 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)

Show sample text content

Rated 4.89 of 5 – based on 25 votes