Last modified: Mon Jun 14 14:19:40 CEST 2010 or later by ingerbo[at]math.uio.no.


Welcome to the seminar page for spring 2010

    The Algebra and Algebraic geometry group

Department of Mathematics, University of Oslo



General information about our mailing list algebra-seminar[at]math.uio.no can be found here.
Seminar history: Spring 2003, Autumn 2003, Spring 2004, Autumn 2004, Spring 2005, Autumn 2005, Spring 2006, Autumn 2006, Spring 2007, Autumn 2007, Spring 2008, Autumn 2008, Spring 2009, Autumn 2009
Fridays 14.00 for 14.30, pausearealet 7. etasje, Felleskollokviet (Department Colloquium). Contact: Bjørn Jahren (bjoernj).

Seminar in Algebra and Algebraic geometry

Time: Mondays 14.15 (lunch at 11.45, 6. floor)
Venue: Seminar room B63, Niels Henrik Abel building
Organiser: Arne B. Sletsjøe (arnebs)

NB!     Next seminar:

11. January Algebra lunch and planning session
18. January Kristian Ranestad (Oslo)
The convex hull of a space curve
Abstract:
The boundary of the convex hull of a compact algebraic curve in real 3-space defines a real algebraic surface. For general curves, that boundary surface is reducible, consisting of tritangent planes and a scroll of stationary bisecants. In recent work with Sturmfels we extend classical formulas to express the degree of this surface in terms of the degree, genus and singularities of the curve. For rational curves we present methods for computing their defining polynomials, and exhibit a range of examples.
25. January Lunch
1. February Lunch (and discussing the seminar series)
8. February Lunch
15. February Lunch
22. February Michal Kapustka (Oslo)
A duality for K3 surfaces of genus 10
1. March Seminar series on Moduli Stacks, talk 1
John Christian Ottem (Oslo)
Introduction and examples
8. March Lunch
15. March Seminar series on Moduli Stacks, talk 2
Jan Christophersen (Oslo)
Etale topology and algebraic spaces
22. March Seminar series on Moduli Stacks, talk 3
Arne B. Sletsjøe (Oslo)
Groupoids and stacks I
29. March Easter break
5. April Easter break
12. April Seminar series on Moduli Stacks, talk 4
Daniel Larsson (HiO)
Groupoids and stacks II
19. April Lunch
26. April Seminar series on Moduli Stacks, talk 5
Geir Ellingsrud (Oslo)
Applications of stacks to moduli questions
3. May Anthony Iarrobino (Northeastern University)
Commuting nilpotent matrices and Artin algebras
Abstract
10. May Helge Maakestad
On the annihilator ideal of a highest weight vector
Abstract:
Let E be a finite dimensional vector space over an algebraically closed field K of characteristic zero and let G=SL(E) be the special linear group on E. Let V be an irreducible finite dimensional G-module with highest weight vector v and highest weight \lambda. Let ann(v) in U(sl(E)) be the left annihilator ideal of v and let ann_l(v) be its canonical filtration. In this talk I will construct a complement
U_l(sl(E)) = U_l(n)\oplus ann_l(v)
of the annihilator ideal ann_l(v). The complement is given by the universal enveloping algebra of a sub Lie algebra n=n(E_*) in sl(E) depending on a flag E_* in E determined by the highest weight \lambda for V. I will use the complement U_l(n) to define a canonical basis for U_l(sl(E))v - the canonical filtration for V. I will also calculate the dimension of U_l(sl(E))v.
The canonical filtration U_l(sl(E))v is related to the fiber of the jet bundle J_l(L)(e) where L in Pic^G(G/P) and P in G is a parabolic subgroup. There is an isomorphism
J_l(L)(e)^* \cong U_l(sl(E))v
of P-modules.
If time permits I will discuss the relationship between the canonical filtration, jet bundles and discriminants of linear systems on flag schemes. To the discriminant of a linear system on any flag scheme one may associate a double complex - the discriminant double complex - and to determine this complex one needs information on the jet bundle. It is hoped the relationship between the jet bundle and the canonical filtration will give enough information on the jet bundle to be able to determine if the discriminant double complex may be used to construct a resolution of the ideal sheaf of the discriminant.
17. May Bank holiday
24. May Bank holiday
31. May Lunch
7. June Abdul Mohammad (Oslo)
Smooth rational surfaces of degree eleven and sectional genus eight in the projective fivespace
14. June Lunch
21. June Lunch