Two constructible functions on the Hilbert scheme of points.
Cancelled
Event details
| Date | 20.12.2012 |
| Hour | 15:15 › 17:00 |
| Speaker | Andrew Morrison, ETHZ |
| Location | |
| Category | Conferences - Seminars |
We discuss the values of two natural functions on the Hilbert scheme of points on a threefold.
The first is given by the dimension of the tangent space. Unlike the Hilbert scheme of points on a surface the moduli scheme in three dimensions is not smooth so the dimension of the tangent space can jump. However we will see that the dimension always jumps by a multiple of two preserving the parity of the constructible function. During the proof we will also see that the commuting variety always has a tangent space of even dimension.
The second integer valued function is the Behrend function. This function associates to a scheme with a symmetric obstruction theory a Donaldson-Thomas type invariant. In the case of the Hilbert scheme of n points on a threefold we show that this function is constant with value (-1)^n. This implies that the components of this Hilbert scheme are generically reduced.
The first is given by the dimension of the tangent space. Unlike the Hilbert scheme of points on a surface the moduli scheme in three dimensions is not smooth so the dimension of the tangent space can jump. However we will see that the dimension always jumps by a multiple of two preserving the parity of the constructible function. During the proof we will also see that the commuting variety always has a tangent space of even dimension.
The second integer valued function is the Behrend function. This function associates to a scheme with a symmetric obstruction theory a Donaldson-Thomas type invariant. In the case of the Hilbert scheme of n points on a threefold we show that this function is constant with value (-1)^n. This implies that the components of this Hilbert scheme are generically reduced.
Practical information
- Informed public
- Free
Organizer
- Tamas Hausel