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Seminar on Convex and Toric Geometry SemesterWiSe 2019 / 20 Lecturer Prof. Dr. Klaus Kuennemann Type of course (Veranstaltungsart) Seminar Contents Toric varieties form an important class of examples of algebraic varieties which can be described purely in terms of convex geometry. The connection between convex geometry and algebraic geometry turns out to be an essential tool to solve difficult problems either in convex geometry or in algebraic geometry. We will follow the book 'Combinatorial Convexity and Algebraic Geometry' by Ewald. In the first part of the seminar we will focus on convex geometry. We will introduce cones, dual cones, monoids, fans, etc. and study their basic properties along with several examples. For this part of the seminar a solid knowledge of linear algebra (LA 1+2) and analysis (Analysis 1+2) is required. In the second part of the seminar we apply the notions from convex geometry introduced in the first part to algebraic geometry by introducing the class of toric varieties. We will see how algebro-geometric statements about toric-varieties can be translated into problems of convex geometry which are sometimes easier to solve. The second part of the seminar is particularly recommended to students interested in algebraic geometry. It requires basic knowledge in algebraic geometry which can be acquired for instance by attending the course 'Algebraic geometry I' simultaneously. Literature Ewald, Guenter. Combinatorial Convexity and Algebraic Geometry. Graduate Texts in Mathematics Vol. 168. Springer Science & Business Media, New York 1996. Time/Date Di 16h00 - 17h30 Location M102 Registration
BSem, MSem, LA-GySem ECTS Siehe Modulkatalog. MV und Nebenfach: 4,5 LP bei Studienbeginn ab WS 15/16, 6 LP bei Studienbeginn vor WS 15/16 |