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Die folgenden Informationen sind noch nicht freigegeben und deshalb unverbindlich: Toric Varieties SemesterSoSe 2026 Lecturer Gari Peralta Type of course (Veranstaltungsart) Vorlesung German title Torische Varietäten Contents This course serves as an introduction to the theory of toric varieties. These are a special kind of algebraic varieties over a field, which can be described explicitly in terms of the combinatorics of objects coming from discrete geometry. Their combinatorial nature makes them suitable for concrete computations on a plethora of examples; a rare feature in algebraic geometry. It is therefore an excellent companion to a course on algebraic geometry. This course aims to cover the content presented in Chapters 1 to 6 of Cox, Little and Schenck's book. This roughly includes the descriptions of normal toric varieties in terms of fans, and their group of torus-invariant divisors/line bundles in terms of piecewise linear functions. If time permits, we may study additional topics, such as intersection theoretic properties, the sheaf cohomology of toric varieties, or the theorem of resolution of singularities. Literature Main reference: D. A. Cox, J. D. Little, H. K. Schenck. Toric varieties. Alternative reference: W. Fulton. Introduction to Toric Varieties. Recommended previous knowledge Basic commutative algebra, for instance, the material covered in Atiyah & Macdonald's book. Some familiarity with algebraic geometry is welcomed. For instance, students that attended the Winter Semester 25/26 Lecture by Marc Hoyois (or any other introductory course on the topic) will fit right in. In any case, the necessary material will be discussed during the lecture. The student might also profit from previous knowledge on discrete geometry, but it is not expected. Time/Date Wednesdays, 14-16 (Lecture) & 16-18 (Tutorial). Location M101 Registration
MV, MArGeo ECTS 4,5 |