Freie Universität Berlin | Fachbereich Mathematik/Informatik | Institut für Mathematik | KVV | Impressum |
Algebraic Geometry I - Schemes and Complex Spaces
This course will be an introduction to the modern formalism of complex algebraic and analytic geometry. Topics include: Homological algebra (modules, abelian categories); Ringed spaces (schemes, complex spaces); Sheaf cohomology. The course will be complemented by a seminar on plane algebraic curves.
Information
Exam
Friday, July 17,
8-10am
A6, SR 032
Literature:
M.F. Atiyah, I.G. Macdonald: Introduction to commutative algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont. 1969, ix+128 pp.
Th. de Jong, G. Pfister: Local analytic geometry. Basic theory and applications, Advanced Lectures in Mathematics, Friedr. Vieweg & Sohn, Braunschweig, 2000, xii+382 pp.
D. Eisenbud, J. Harris: The geometry of schemes. Graduate Texts in Mathematics. 197. New York, NY: Springer. x+294 p.
R. Godement: Topologie algébrique et théorie des faisceaux. Actualites scientifiques et industrielles. 1252. Publications de l'Institut de Mathematique de l'Universite de Strasbourg. XIII. Paris: Hermann. VIII, 283 p.
A Grothendieck, J. Dieudonné: Éléments de géométrie algébrique (EGA). I-IV. Publ. Math. Inst. Hautes Étud. Sci. 4, 8, 11, 17, 20, 24, 28, 32. Freely available at numdam.org.
G. Harder: Lectures on algebraic geometry I. Sheaves, cohomology of sheaves, and applications to Riemann surfaces, Aspects of Mathematics, E 35, Wiesbaden: Vieweg, 2008, xi+290 pp.
R. Hartshorne: Algebraic geometry, Corr. 3rd printing, Graduate Texts in Mathematics, 52, New York-Heidelberg-Berlin: Springer- Verlag, 1983, xvi+496 pp.
D. Huybrechts: Complex geometry. An introduction, Universitext, Berlin: Springer, 2005, xii+309 pp.
A. Neeman: Algebraic and analytic geometry, London Mathematical Society Lecture Note Series, 345, Cambridge University Press, Cambridge, 2007, xii+420 pp.
B. Pareigis: Kategorien und Funktoren, Teubner Verlag, 1969, 192 pp.
J.-P. Serre: Faisceaux algébriques cohérents (FAC). Ann. Math. (2) 61, 197-278 (1955). (Also included in Serre's Œuvres, Springer)
I.R. Shafarevich: Basic algebraic geometry. 2: Schemes amd complex manifolds, Transl. from the Russian by Miles Reid, 2nd, rev. and exp. ed., Berlin: Springer-Verlag, 1994, xv+269 pp.
J.L. Taylor: Several complex variables with connections to algebraic geometry and Lie groups, Graduate Studies in Mathematics, 46, American Mathematical Society, Providence, RI, 2002, xvi+507 pp.
Problem Sets
Set
Download
Set
Download
Set
Download
1
5
9
2
6
10
3
7
11
4
8