Toric Varieties
Toric varieties provide a sort of elementary way to see many examples and phenomena in algebraic geometry, partly due to its close connections with simplicial geometry. As noted by Fulton: “toric varieties have provided a remarkably fertile testing ground for general theories”, the concreteness of toric varieties offers an excellent context for someone encountering the powerful techniques of modern algebraic geometry for the first time.
In this course, I will give a basic introduction to the properties of toric varieties, with many examples, and then concentrate on the cohomology of sheaves and intersection theory on toric varieties.
In this course, I will give a basic introduction to the properties of toric varieties, with many examples, and then concentrate on the cohomology of sheaves and intersection theory on toric varieties.
Lecturer
Date
4th March ~ 27th May, 2024
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Monday | 13:30 - 15:05 | A3-1a-204 | ZOOM 08 | 787 662 9899 | BIMSA |
| Wednesday | 09:50 - 11:25 | A3-1a-205 | ZOOM 08 | 787 662 9899 | BIMSA |
Prerequisite
Basic knowledge of algebraic varieties
Syllabus
(1) Definitions and examples
(2) Divisors on toric varieties
(3) Projective toric morphism
(4) Sheaf cohomology of toric varieties
(5) Intersection theory
(2) Divisors on toric varieties
(3) Projective toric morphism
(4) Sheaf cohomology of toric varieties
(5) Intersection theory
Reference
[1] D. Cox, J. Little, H. Schenck, Toric varieties, Grad. Stud. Math. 124, American Mathematical Society, Providence, RI, 2011. xxiv+841 pp.
[2] W. Fulton, Introduction to toric varieties, Ann. of Math. Stud. 131, Princeton University Press, Princeton, NJ, 1993. xii+157 pp.
[3] T. Oda, Convex bodies and algebraic geometry. An introduction to the theory of toric varieties. Translated from the Japanese. Ergeb. Math. Grenzgeb. (3), Springer-Verlag, Berlin, 1988. viii+212 pp.
[2] W. Fulton, Introduction to toric varieties, Ann. of Math. Stud. 131, Princeton University Press, Princeton, NJ, 1993. xii+157 pp.
[3] T. Oda, Convex bodies and algebraic geometry. An introduction to the theory of toric varieties. Translated from the Japanese. Ergeb. Math. Grenzgeb. (3), Springer-Verlag, Berlin, 1988. viii+212 pp.
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
Dali Shen is an assistant professor at BIMSA currently. His research is focused on algebraic geometry and complex geometry. He obtained his PhD from Utrecht University. Before joining BIMSA, he held postdoc positions at IMPA and TIFR.