Universität Wien

250093 VO Singularities of Algebraic Varieties (2020W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

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Details

Language: German

Lecturers

Classes (iCal) - next class is marked with N

The course is now scheduled in presence on Wednesdays, 11:30 - 13:00, in SR 12.

  • Wednesday 07.10. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 14.10. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 21.10. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 28.10. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 04.11. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 11.11. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 18.11. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 25.11. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 02.12. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 09.12. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 16.12. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 13.01. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 20.01. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 27.01. 11:30 - 13:00 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

Singularities of algebraic or analytic varieties are points where the variety is not smooth, i.e., not locally diffeomorphic to a linear space. Examples of surface with singularities can be seen on

https://homepage.univie.ac.at/herwig.hauser/gallery.html

The study of these singular points is important for understanding the geometry and properties of varieties, both real and complex and, on the arithmetic side, over finite fields. It combines techniques from algebra, analysis and differential geometry. We will discuss tangent spaces, deformations, symmetry groups, hyperplane sections and the resolution of singularities by normalization and blowups. The course shall prepare to write Master's theses on related topics.

Assessment and permitted materials

Oral exam.

Minimum requirements and assessment criteria

Examination topics

Reading list

E. Faber, H. Hauser: Today's Menu: Geometry and Resolution of Singular Algebraic Surfaces. Bulletin Amer. Math. Soc. 2010, available at www.hh.hauser.cc

Association in the course directory

MGEV, MALV

Last modified: Tu 13.10.2020 11:50