Rahul Pandharipande: Catalogue data in Spring Semester 2016
|Name||Prof. Dr. Rahul Pandharipande|
Professur für Mathematik
ETH Zürich, HG G 55
|Telephone||+41 44 632 56 89|
|401-3146-12L||Algebraic Geometry||10 credits||4V + 1U||R. Pandharipande|
|Abstract||This course is an Introduction to Algebraic Geometry (algebraic varieties and schemes).|
|Literature||The main reference for the course is |
* Robin Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, Springer.
For the exercises we will also use
* Joe Harris, Algebraic Geometry, A First Course, Graduate Texts in Mathematics, Springer.
There are also some very good texts that are freely available online. I recommend two of them:
* J.S. Milne, Algebraic Geometry, http://www.jmilne.org/math/CourseNotes/AG.pdf (mainly about abstract algebraic varieties - schemes only appear in the very end)
* Ravi Vakil, Foundations of Algebraic Geometry, http://math.stanford.edu/~vakil/216blog/ (quite abstract)
* I. R. Shafarevich, Basic Algebraic geometry 1 & 2, Springer-Verlag.
* Ulrich Görtz and Torsten Wedhorn, Algebraic Geometry I, Advanced Lectures in Mathematics, Springer.
* Jean Gallier and Stephen S. Shatz, Algebraic Geometry http://www.cis.upenn.edu/~jean/algeom/steve01.html
|Prerequisites / Notice||Requirement: Commutative Algebra course.|
|401-5000-00L||Zurich Colloquium in Mathematics||0 credits||W. Werner, P. L. Bühlmann, M. Burger, S. Mishra, R. Pandharipande, University lecturers|
|401-5140-11L||Algebraic Geometry and Moduli Seminar||0 credits||2K||R. Pandharipande|
Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.
Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
|6 credits||13R||R. Pandharipande|
|Abstract||Complex functions of one variable, Cauchy-Riemann equations, Cauchy theorem and integral formula, singularities, residue theorem, index of closed curves, analytic continuation, conformal mappings, Riemann mapping theorem.|
|Literature||L. Ahlfors: "Complex analysis. An introduction to the theory of analytic functions of one complex variable." International Series in Pure and Applied Mathematics. McGraw-Hill Book Co.|
B. Palka: "An introduction to complex function theory."
Undergraduate Texts in Mathematics. Springer-Verlag, 1991.
R.Remmert: Theory of Complex Functions.. Springer Verlag
E.Hille: Analytic Function Theory. AMS Chelsea Publication
|Prerequisites / Notice||The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.|