Tropical Algebraic Geometry
By: Itenberg, Ilia [author.].
Contributor(s): Mikhalkin, Grigory [author.1] | Shustin, Eugenii [author.2] | SpringerLink (Online service)0.
Material type:
BookSeries: Oberwolfach Seminars ; 350.Publisher: Basel : Birkh�user Basel, 2007. Description: VIII, 104 p. 30 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783764383107.Subject(s): Mathematics | Algebraic geometry.1 | Mathematics.2 | Algebraic Geometry.1DDC classification: 516.35 Online resources: Click here to access online | Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
|---|---|---|---|---|---|---|
| PK Kelkar Library, IIT Kanpur | Available | EBK9393 |
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.
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.
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