| Language |
English
|
| From |
2011/11/18 13:30
|
| To |
2011/11/18 15:00
|
| Place | Room 108, Building No.3, Faculty of Science, Kyoto University |
| Seminar Name | Algebra Geometrical Seminar |
| Title |
Relative spherical objects |
| Field |
Algebra
Geometry
|
| Speakers | Timothy Logvinenko |
| Affiliation | Warwick |
| Abstract | Seidel and Thomas introduced some years ago a notion of a
spherical object in the derived category D(X) of a smooth projective
variety X. Such objects induce, in a simple way, auto-equivalences of D(X)
called 'spherical twists'. In a sense, they are mirror-symmetric analogues
of Lagrangian spheres on a symplectic manifold and the induced
auto-equivalences mirror the Dehn twists associated with the latter. We
generalise this notion to the relative context by explaining what does it
mean for an object of D(Z x X) to be _spherical over Z_ for any two
separated schemes Z and X of finite type. Such objects induce naturally
two
auto-equivalences: one of D(X), called "the twist", and the other of D(Z)
called "the co-twist". For objects of D(Z x X) which are orthogonal over Z
we give a simple cohomological criterion for being spherical over Z which
resembles the original definition of Seidel and Thomas. This is a joint
work with Rina Anno (UMass/Amherst). |
| Link | http://www.math.kyoto-u.ac.jp/~mhyo/agsem/agseminar.html |
|