Universität Wien

250116 VO Graded Rings and Projective Geometry (2023S)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

Wednesday 01.03. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 08.03. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 15.03. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 22.03. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 29.03. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 19.04. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 26.04. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 03.05. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 10.05. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 17.05. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 24.05. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 31.05. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 07.06. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 14.06. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 21.06. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 28.06. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

The purpose of this course is to introduce methods to study projective varieties in (weighted) projective space via looking at the algebraic structure of the associated graded coordinate ring. Numerical invariants of the ring (its Hilbert function, so-called Hilbert numerator, etc) are related to the underlying space via Riemann-Roch type theorems. Algebraic structures of the ring (whether it is Cohen-Macaulay, Gorenstein, etc) are reflected in geometric properties of the embedding. The course will be very much examples-based; we will recall, and build up, the theory as we go along.

Assessment and permitted materials

Written examination or oral presentation.

Minimum requirements and assessment criteria

Familiarity with basic notions of projective algebraic geometry will be assumed. All other concepts and necessary background results will be explained during the course.

Examination topics

All topics covered in the lectures.

Reading list

W. Bruns and J. Herzog, Cohen-Macaulay Rings, Revised Edition, CUP, Chapters 1-4
D. Eisenbud, Commutative algebra with a View toward Algebraic Geometry, Springer, Chapter 1
A. R. Iano-Fletcher, Working with weighted complete intersections, in Explicit birational geometry of 3-folds, A. Corti and M. Reid (editors), CUP
M. Reid, Graded rings and varieties in weighted projective space, available at https://homepages.warwick.ac.uk/~masda/surf/more/grad.pdf

Association in the course directory

MALV

Last modified: Tu 03.10.2023 09:28