Last updated July 2008 by ingerbo[at]

Welcome to the seminarpage for autumn 2008

    The Algebra and Algebraic Geometry group

Department of Mathematics, University of Oslo

General information about our mailing list algebra-seminar[at] 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
Fridays 14.00 for 14.30, pausearealet 7. etasje, Felleskollokviet (Department Colloquium). Contact: Bjørn Jahren (bjoernj).

Seminar in Algebra and Algebraic Geometry

Time: Mondays 12.15 (lunch at 11.45, 6. floor)
Venue: Seminar room B63, Niels Henrik Abel building
Organiser: Arne B. Sletsjøe (arnebs)

NB!     Next seminar: 8.-9. December: Lutefisk-seminars

25. August Olav Arnfinn Laudal (Oslo)
Non-commutative deformation theory, algebraic geometry, quantum fields and quarks, I
1. September Olav Arnfinn Laudal (Oslo)
Non-commutative deformation theory, algebraic geometry, quantum fields and quarks, II
8. September Olav Arnfinn Laudal (Oslo)
Non-commutative deformation theory, algebraic geometry, quantum fields and quarks, III
15. September Ragni Piene (Oslo)
Classifying smooth lattice polytopes via toric fibrations I
Let P be a convex n-dimensional lattice polytope in R^n. Its codegree is the smallest integer m such that mP has interior lattice points. Cayley polytopes are examples of polytopes with large codegree. In a joint work with A. Dickenstein and S. Di Rocco we partially answer a question of Batyrev and Nill, by showing that all smooth Q-normal polytopes with codegree at least (n+3)/2 are strict Cayley polytopes. Our proof relies on the study of the nef value and the nef value map of a nonsingular polarized toric variety (X,L).
22. September Ragni Piene (Oslo)
Classifying smooth lattice polytopes via toric fibrations II
29. September Algebra lunch
6. October Algebra lunch
13. October David Rydh (KTH, Stockholm)
Families of cycles
The Chow variety, parameterizing cycles on a projective space, was introduced by Chow and van der Waerden in 1937 but its functorial aspects are still not well understood. In this talk I will define, in any characteristic, a functor parameterizing cycles which is closely related to the Chow variety. It (conjecturally in some cases) generalizes the functorial descriptions of Barlet, Ang\'eniol, Guerra, Koll\'ar and Suslin-Voevodsky. It also explains related work by Mumford and Fogarty.
20. October Edoardo Sernesi (Roma)
The curve of lines on a Fano 3-fold of genus 8
I will report on joint work with F. Flamini in which we prove a variant of Torelli's theorem for Fano 3-folds of genus 8 based on the geometry of the curve of lines on the 3-fold.
27. October Kristian Ranestad (Oslo)
Toric polar Cremona transformations
30.-31. October Nasjonalt algebramøte
3. November Algebra lunch
10. November David Eklund (KTH, Stockholm)
Algebraic C*-actions and homotopy continuation
Let X be a smooth projective variety over C equipped with a C*-action whose fixed points are isolated. Let Y and Z be subvarieties of X of complementary dimensions in X. I will present a method for approximating the isolated points of intersection between Y and Z based on homotopy continuation and the Bialynicki-Birula decompositions of X into locally closed invariant subsets. The method was developed with applications to mechanics in mind and I will explain how it gives a new solution to the inverse kinematic problem of a so-called six-revolute serial-link mechanism.
17. November Arne B. Sletsjøe (Oslo)
Deformasjoner under bibetingelser
24. November Algebra lunch
1. December Algebra lunch
8.-9. December, B63 Lutefisk-seminars in B63 (both days):

Monday 8.:
11.45: Algebra lunch (6.etg NHA)

12.15: Dan Laksov (KTH)
Splitting algebraer
Vi gir definisjoner, konstruksjoner, og egenskaper til splitting algebraer.

13.15: Stephanie Yang (KTH)
Faber-type conjectures on moduli spaces of curves
In this talk I will review Faber's conjectures and known results concerning tautological rings of moduli spaces of curves, and describe recent attempts to extend these to other moduli spaces.

19.30: Dinner, Rorbua (Aker Brygge) Lutefisk/juletallerken

Tuesday 9.:
10.15: Sandra Di Rocco (KTH)
Some results on reducible hyperplane sections
A cone with vertex a point in projective space has the property that every hyperplane section through the vertex is reducible. How restrictive is to ask that given an (ample and spanned) linear system |L| on a variety X, there is at least a point, x, such that all elements passing through x are reducible or non reduced? The possibilities are indeed very limited, X is a surface and it is mapped by |L| to a cone. This is work of Bertni, Besana-Di Rocco-Lanteri and Lanteri-De Fernex. I will report on some recent work, with Besana-Lanteri, concerning linear systems whose elements passing through higher degree zero-schemes are reducible. In particular how big can the locus of such "bad zero-schemes" be in the appropriate Hilbert scheme?

11.15:Roy Skjelnes (KTH)
Parameterizing distinct points in a variety.
Let H denote the Hilbert scheme parameterizing n points on a separated algebraic space X over an arbitrary base space. Using sheaf theoretical methods it is easy to construct the open subspace U of H parameterizing distinct points. However, by studying the space U locally one obtains, surprisingly enough, information about how distinct points degenerates. This information can be used to construct the schematic closure of U in H, which in fact was done recently in a joint work with David Rydh.