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Author : David Eisenbud
Release : 2016-04-14
Genre : Mathematics
Kind : eBook
Book Rating : 084/5 ( reviews)
Book Synopsis 3264 and All That by : David Eisenbud
Download or read book 3264 and All That written by David Eisenbud. This book was released on 2016-04-14. Available in PDF, EPUB and Kindle. Book excerpt: 3264, the mathematical solution to a question concerning geometric figures.
Author : David Eisenbud
Release : 2006-04-06
Genre : Mathematics
Kind : eBook
Book Rating : 397/5 ( reviews)
Book Synopsis The Geometry of Schemes by : David Eisenbud
Download or read book The Geometry of Schemes written by David Eisenbud. This book was released on 2006-04-06. Available in PDF, EPUB and Kindle. Book excerpt: Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.
Author : Donu Arapura
Release : 2012-02-15
Genre : Mathematics
Kind : eBook
Book Rating : 097/5 ( reviews)
Book Synopsis Algebraic Geometry over the Complex Numbers by : Donu Arapura
Download or read book Algebraic Geometry over the Complex Numbers written by Donu Arapura. This book was released on 2012-02-15. Available in PDF, EPUB and Kindle. Book excerpt: This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject. It covers sheaf theory, cohomology, some Hodge theory, as well as some of the more algebraic aspects of algebraic geometry. The author frequently refers the reader if the treatment of a certain topic is readily available elsewhere but goes into considerable detail on topics for which his treatment puts a twist or a more transparent viewpoint. His cases of exploration and are chosen very carefully and deliberately. The textbook achieves its purpose of taking new students of complex algebraic geometry through this a deep yet broad introduction to a vast subject, eventually bringing them to the forefront of the topic via a non-intimidating style.
Author : Robin Hartshorne
Release : 2009-11-12
Genre : Mathematics
Kind : eBook
Book Rating : 966/5 ( reviews)
Book Synopsis Deformation Theory by : Robin Hartshorne
Download or read book Deformation Theory written by Robin Hartshorne. This book was released on 2009-11-12. Available in PDF, EPUB and Kindle. Book excerpt: The basic problem of deformation theory in algebraic geometry involves watching a small deformation of one member of a family of objects, such as varieties, or subschemes in a fixed space, or vector bundles on a fixed scheme. In this new book, Robin Hartshorne studies first what happens over small infinitesimal deformations, and then gradually builds up to more global situations, using methods pioneered by Kodaira and Spencer in the complex analytic case, and adapted and expanded in algebraic geometry by Grothendieck. The author includes numerous exercises, as well as important examples illustrating various aspects of the theory. This text is based on a graduate course taught by the author at the University of California, Berkeley.
Author : William Fulton
Release : 1993
Genre : Mathematics
Kind : eBook
Book Rating : 497/5 ( reviews)
Book Synopsis Introduction to Toric Varieties by : William Fulton
Download or read book Introduction to Toric Varieties written by William Fulton. This book was released on 1993. Available in PDF, EPUB and Kindle. Book excerpt: Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic geometry notions such as singularities, birational maps, cycles, homology, intersection theory, and Riemann-Roch translate into simple facts about polytopes, toric varieties provide a marvelous source of examples in algebraic geometry. In the other direction, general facts from algebraic geometry have implications for such polytopes, such as to the problem of the number of lattice points they contain. In spite of the fact that toric varieties are very special in the spectrum of all algebraic varieties, they provide a remarkably useful testing ground for general theories. The aim of this mini-course is to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications. The text concludes with Stanley's theorem characterizing the numbers of simplicies in each dimension in a convex simplicial polytope. Although some general theorems are quoted without proof, the concrete interpretations via simplicial geometry should make the text accessible to beginners in algebraic geometry.
