Algebraic Stacks

Dozent: Prof. Dr. Urs Hartl

Sprechstunde: Freitag 10:00 - 11:00 Uhr

Vorlesungszeit: Montag 10:00 - 12:00 Uhr in N 1

Kommentar:

In algebraic geometry one is often interested in having moduli spaces of objects in the sense that the objects are parameterized by the points in the moduli space. In many important cases these moduli spaces cannot be algebraic varieties or schemes. The concept of algebraic stacks solves this problem. In the lecture we will develop the theory of algebraic stacks and present the application to moduli spaces of projective curves and to moduli spaces of vector bundles on a fixed projective curve.

Literatur:

D. Edidin: What is... a Stack?, Notices of the AMS 50 (2003), 458-459
B. Fantechi: Stacks for everybody, European Congress of Mathematics (Barcelona, 2000), Volume I, Progr. Math., 201, Birkhäuser, Basel, 2001, pp. 349-359.
J. Alper: A Guide to the Literature on Algebraic Stacks.
Wikipedia article on Stacks.
Wikipedia article on Moduli Spaces.
P. Deligne, D. Mumford: The Irreducibility of the Space of Curves of Given Genus, Publ. Math. IHES 36 (1969), 75-110.
D. Edidin: Notes on the construction of the moduli space of curves, in "Recent progress in intersection theory" (Bologna, 1997), Trends Math., pp. 85-113. Birkhäuser, Boston, MA, 2000.
T. Gómez: Algebraic stacks, Indian Academy of Sciences. Proceedings. Mathematical Sciences, 111 (2001), 1-31.
G. Laumon, L. Moret-Bailly: Champs algébriques, Ergebnisse 39, Springer-Verlag, Berlin etc. 2000.
M. Olsson: Algebraic spaces and stacks, Colloquium Publications 62, American Mathematical Society, 2016.

Weitere Literatur:

D. Eisenbud, J. Harris: The Geometry of Schemes, GTM 197, Springer-Verlag, 2000.
[GIT] D. Mumford, J. Fogarty, F. Kirwan: Geometric Invariant Theory, Ergebnisse 34, Springer-Verlag, 1994.

Zielgruppe:

Doktoranden und interessierte Masterstudierende

Diese Veranstaltung ist für Masterstudierende nicht im Studium anrechenbar.