By David A. Cox
Toric kinds shape a stunning and obtainable a part of smooth algebraic geometry. This booklet covers the normal issues in toric geometry; a unique function is that every of the 1st 9 chapters comprises an introductory part at the worthwhile history fabric in algebraic geometry. different themes coated comprise quotient buildings, vanishing theorems, equivariant cohomology, GIT quotients, the secondary fan, and the minimum version application for toric types. the topic lends itself to wealthy examples mirrored within the 134 illustrations incorporated within the textual content. The publication additionally explores connections with commutative algebra and polyhedral geometry, treating either polytopes and their unbounded cousins, polyhedra. There are appendices at the background of toric kinds and the computational instruments on hand to enquire nontrivial examples in toric geometry. Readers of this ebook may be accustomed to the fabric coated in easy graduate classes in algebra and topology, and to a just a little lesser measure, complicated research. additionally, the authors suppose that the reader has had a few past event with algebraic geometry at a complicated undergraduate point. The publication may be an invaluable reference for graduate scholars and researchers who're attracted to algebraic geometry, polyhedral geometry, and toric types.
Read Online or Download Toric Varieties (Graduate Studies in Mathematics) PDF
Similar Algebraic Geometry books
This paintings attracts jointly rules from algebraic topology, practical research and geometry. it's a instrument - a method of conveying info between those 3 topics - and it's been used with luck to find theorems throughout a large span of arithmetic. the aim of this booklet is to acquaint the reader with the fundamental principles of analytic K-homology and boost a few of its functions.
In providing a close learn of the geometry and topology of various sessions of "generic" singularities, Geometry of Topological balance bridges the distance among algebraic calculations and continuity arguments to element the mandatory and enough stipulations for a C (infinity) to be C]0-stable. all through, the authors masterfully study this crucial topic utilizing effects culled from a vast diversity of mathematical disciplines, together with geometric topology, stratification idea, algebraic geometry, and commutative algebra.
In response to a graduate path on the Technische Universität, Berlin, those lectures current a wealth of fabric at the glossy conception of convex polytopes. the easy exposition beneficial properties many illustrations, and whole proofs for many theorems. With in basic terms linear algebra as a prerequisite, it takes the reader speedy from the fundamentals to subject matters of modern examine.
The category idea of algebraic types is the focal point of this ebook. This very lively quarter of study continues to be constructing, yet an awesome volume of data has accrued over the last two decades. The authors target is to supply an simply available creation to the topic. The ebook begins with preparatory and conventional definitions and effects, then strikes directly to talk about a variety of points of the geometry of gentle projective kinds with many rational curves, and finishes in taking the 1st steps in the direction of Moris minimum version software of type of algebraic forms by means of proving the cone and contraction theorems.
Additional resources for Toric Varieties (Graduate Studies in Mathematics)