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OverviewTropical 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 DetailsAuthor: Ilia Itenberg , Grigory Mikhalkin , Eugenii I. ShustinPublisher: Birkhauser Verlag AG Imprint: Birkhauser Verlag AG Volume: v. 35 Dimensions: Width: 17.00cm , Height: 0.80cm , Length: 24.00cm Weight: 0.259kg ISBN: 9783764383091ISBN 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  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 ContentsPreface.- 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.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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