Algebraic Curves
Algebraic geometry is the study of solutions of polynomial equations, and has close connections with other areas of mathematics.
In this course, I will give a basic introduction to algebraic varieties, focusing on using curves (the dimension one case) to illustrate the basic notions in algebraic geometry.
In this course, I will give a basic introduction to algebraic varieties, focusing on using curves (the dimension one case) to illustrate the basic notions in algebraic geometry.
Lecturer
Date
23rd September ~ 18th December, 2024
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Monday | 13:30 - 15:05 | A3-1a-204 | ZOOM 07 | 559 700 6085 | BIMSA |
| Wednesday | 09:50 - 11:25 | A3-1a-204 | ZOOM 07 | 559 700 6085 | BIMSA |
Prerequisite
Basic knowledge of polynomials, rings and ideals.
Syllabus
(1) Affine and projective varieties
(2) Local properties of curves
(3) Morphisms of varieties
(4) Resolution of singularities
(5) Riemann-Roch theorem
(2) Local properties of curves
(3) Morphisms of varieties
(4) Resolution of singularities
(5) Riemann-Roch theorem
Reference
[1] E. Arbarello, M. Cornalba, P. A. Griffiths, J. Harris, Geometry of algebraic curves, Vol. I, Grundlehren Math. Wiss., 267, Springer-Verlag, New York, 1985. xvi+386 pp.
[2] W. Fulton, Algebraic curves, An introduction to algebraic geometry, Notes written with the collaboration of Richard Weiss, Reprint of 1969 original, Adv. Book Classics, Addison-Wesley Publishing Company, Advanced Book Program, Redwood City, CA, 1989. xxii+226 pp.
[3] Phillip A. Griffiths, Introduction to algebraic curves, Translated from the Chinese by Kuniko Weltin, Transl. Math. Monogr., 76, American Mathematical Society, Providence, RI, 1989. x+221 pp.
[2] W. Fulton, Algebraic curves, An introduction to algebraic geometry, Notes written with the collaboration of Richard Weiss, Reprint of 1969 original, Adv. Book Classics, Addison-Wesley Publishing Company, Advanced Book Program, Redwood City, CA, 1989. xxii+226 pp.
[3] Phillip A. Griffiths, Introduction to algebraic curves, Translated from the Chinese by Kuniko Weltin, Transl. Math. Monogr., 76, American Mathematical Society, Providence, RI, 1989. x+221 pp.
Video Public
Yes
Notes Public
No
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.