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Tropical Algebraic Geometry

Tropical Algebraic Geometry
Catalogue Information
Field name Details
Dewey Class 516.35 (DDC 23)
Title Tropical Algebraic Geometry (EB) / by Illia Itenberg, Grigory Mikhalkin, Eugenii Shustin.
Author Itenberg, Illia
Added Personal Name Mikhalkin, Grigory author.
Shustin, Eugenii author.
Other name(s) SpringerLink (Online service)
Publication Basel : : Birkhäuser Basel, , 2009.
Physical Details : online resource.
Series Oberwolfach Seminars ; 35
ISBN 9783034600484
Summary Note 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.:
Contents note 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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