Last modified: Tue Nov 30 21:41:53 CET 2010 or later by ingerbo[at]math.uio.no.


Welcome to the seminar page for autumn 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, Spring 2010
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 12.00, 6. floor)
Venue: Seminar room B63, Niels Henrik Abel building
Organiser: Arne B. Sletsjøe (arnebs)

NB!     Next seminar: 6. December: Elisa Postinghel

23. August Algebra lunch and planning session at 12.00
30. August Algebra lunch
NB! 2. September
Seminar room 534
14.15-15.15
Roland Abuaf (Grenoble)
The singularities of the projective dual: some new perspectives
Abstract:
The study of the singularities of the projective dual apparently started in the 80's with Dimca's celebrated formula. Since then, Parusinski, and after Aluffi-Cukierman, found closed formulas to express the multiplicity of any point in the dual of a smooth projective variety. Unfortunately, these formulas require technical computations in the Chow ring of the variety, which often seem impossible to be carried out. In this talk, I will discuss some recent results that decribe the multiplicity of a point in the dual in terms of 'simple and geometric' invariants of its tangency locus. The techniques developed to prove these results seem to be very promising and could be applied in order to work out an interesting conjecture stated by Ranestad and Sturmfels.
6. September Algebra lunch
NB! 7. September
CMA Guest Lecture
Seminar room B1036
10.15-11.00
CANCELLED
David Eisenbud (Berkeley) Vector bundles and free resolutions
Abstract:
Free resolutions of graded modules over polynomial rings are a way of generalizing the solutions of a system of linear equations over a field. Their study was initiated by David Hilbert as a way of obtaining invariants of projective algebraic varieties. Vector Bundles on projective spaces are a different way of encoding the solution of systems of linear equations with varying coefficients. A group of remarkable conjectures about free resolutions by Boij and Soederberg in 2006 suggested a novel way of thinking about graded modules and set off a wave of activity. The conjectures have now been proven, and themselves greatly extended. The proofs have led, among other things, to a still mysterious duality between a description of the numerical invariants that are possible for the free resolution of a graded module on one side, and the numerical invariants of the cohomology of a vector bundle on projective space on the other. As a result we now have far more precise understanding of both these geometrically important objects.
I will try to give an accessible description of this new work.
13. September Kristian Ranestad (Oslo)
Grassmannembeddinger av Fanovarieteter av genus 10
Sammendrag:
Jeg vil vise hvordan en Fano 4-fold av genus 10 er et lineært snitt av G(2,7) og av G(3,6) og gi noen anvendelser av dette. Resultatene er blitt til i samarbeid med Michal Kapustka.
20. September John Christian Ottem (Oslo/Cambridge)
Elliptiske K3-flater, GIT og Cox ringer
Sammendrag:
Coxringen til en projektiv varietet X generaliserer Cox' homogene koordinatring for toriske varieteter og kan brukes til å uttrykke X som en GIT-kvotsient av en kvasiaffin varietet med en torus. I tilfellet der X er en K3 flate med to elliptiske pensler, kan denne realisasjonen brukes til å studere resolusjonen til Coxringen eksplisitt.
27. September Kristian Moi (Oslo)
E.C.(Etale Cohomology)-seminar, part 1
Etale morfier og topologi/Den lokale ringen (Hensel)/Def. av etale kohomologi
NB! 27. September
4.15p.m., VB,
Science Library-'kick-off'
Marcus du Sautoy (Oxford)
Symmetry: reality's riddle
4. October Arne B. Sletsjøe (Oslo)
E.C.(Etale Cohomology)-seminar, part 2
Knipper og knippekohomologi for etale topologien
11. October Peter Arndt (Oslo)
E.C.(Etale Cohomology)-seminar, part 3
H^1(X_et, -)
18. October María-Cruz Fernández-Fernández (Sevilla/Oslo)
On the irregularity of hypergeometric D-modules
Abstract:
Hypergeometric D-modules were introduced by Gelfand, Graev, Kapranov and Zelevinsky and they arise naturally from toric varieties. They are systems of linear partial differential equations in several complex variables associated with a full rank matrix A with integer entries and a vector of complex parameters. In this talk, we will study the irregularity of such a system by describing their Gevrey series solutions at singular points along coordinate subspaces in a combinatorial way.
25. October Jan Christophersen (Oslo)
E.C.(Etale Cohomology)-seminar, part 4
Beregninger og sammenlikningsteoremer
1. November Geir Ellingsrud (Oslo)
E.C.(Etale Cohomology)-seminar, part 5
Etale kohomologi av kurver
8. November Lars Halvard Halle (Oslo)
E.C.(Etale Cohomology)-seminar, part 6
Tate formodningen I
11.-12. November, in Bergen Nasjonalt algebramøte
15. November Lars Halvard Halle (Oslo)
E.C.(Etale Cohomology)-seminar, part 7
Tate formodningen II
22. November Algebra lunch
29. November Nathan Ilten (Bonn)
Partial smoothings of projective toric Fano varieties
Abstract:
K. Altmann has shown how to construct homogeneous deformations of affine toric varieties using combinatorial techniques. In joint work with R. Vollmert, we describe the fibers of these deformations, in particular, the singularities which occur. Following an idea of A. Mavlyutov, I show how in special situations we can find a flat family simultaneously inducing several of these homogeneous deformations. Combining this with our description of the fibers leads to a sufficient condition for a projective toric Fano variety to have a smoothing in some fixed codimension.
6. December Elisa Postinghel (Oslo)
Toric degenerations of toric surfaces and k-secant degree
Abstract:
There is a long tradition within algebraic geometry that studies the secant varieties. Let X in P^r be the projective toric surface associated to any plane polytope P. We show how informations about the variety of k-secant (k-1)-planes to X can be derived from planar toric degenerations of X, which correspond to regular triangulations D of P. A lower bound to the k-secant degree, by means of the combinatorial geometry of D, is established for k=2,3. This improves a result by B. Sturmfels and S. Sullivant.