Universität Regensburg   IMPRESSUM   DATENSCHUTZ
Fakultät für Mathematik Universität Regensburg
Seminar on Convex and Toric Geometry
Semester
WiSe 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
  • Organisational meeting/distribution of topics: Wednesday, July 24nd at 11h00 in room M201. If
    you are interested to participate in the seminar you may also contact me by email.
  • Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)
  • Presentation: Giving a seminar talk of roughly 90 minutes
Examination (Prüfungsleistungen)
  • Detailed written report of the seminar talk
Regelungen bei Studienbeginn vor WS 2015 / 16
  • Benotet:
    • O. g. Studienleistung und o. g. Prüfungsleistung; die Note ergibt sich aus der Prüfungsleistung
  • Unbenotet:
    • O. g. Studienleistung und Bestehen der o. g. Prüfungsleistung
Modules
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