Tropical Algebraic Geometry
Author:   Ilia Itenberg ,  Grigory Mikhalkin ,  Eugenii I. Shustin
Publisher:   Birkhauser Verlag AG
Volume:   v. 35
ISBN:  

9783764383091


Pages:   111
Publication Date:   16 February 2007
Format:   Paperback
Availability:   Out of stock   Availability explained
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Tropical Algebraic Geometry


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Overview

Tropical geometry is algebraic geometry over the semifield of tropical numbers, i.e., the real numbers and negative infinity enhanced with the (max,+)-arithmetics. Geometrically, tropical varieties are much simpler than their classical counterparts. Yet they carry information about complex and real varieties. These notes present an introduction to tropical geometry and contain some applications of this rapidly developing and attractive subject. It consists of three chapters which complete each other and give a possibility for non-specialists to make the first steps in the subject which is not yet well represented in the literature. The intended audience is graduate, post-graduate, and Ph.D. students as well as established researchers in mathematics.

Full Product Details

Author:   Ilia Itenberg ,  Grigory Mikhalkin ,  Eugenii I. Shustin
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Volume:   v. 35
Dimensions:   Width: 17.00cm , Height: 0.80cm , Length: 24.00cm
Weight:   0.259kg
ISBN:  

9783764383091


ISBN 10:   3764383097
Pages:   111
Publication Date:   16 February 2007
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock   Availability explained
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

Preface.- 1. Introduction to tropical geometry - Images under the logarithm - Amoebas - Tropical curves.- 2. Patchworking of algebraic varieties - Toric geometry - Viro's patchworking method - Patchworking of singular algebraic surfaces - Tropicalization in the enumeration of nodal curves.- 3. Applications of tropical geometry to enumerative geometry - Tropical hypersurfaces - Correspondence theorem - Welschinger invariants.- Bibliography.

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