29/06/2009, 14:00 — 15:00 — Room P3.10, Mathematics Building
Kai Behrend, University of British Columbia
Moduli Spaces via differential graded Lie algebras
I will explain how many interesting moduli spaces in algebraic
geometry can be constructed as the solution set of the
Maurer-Cartan equation in a differential graded Lie algebra, modulo
the action of the gauge group. The advantage of this approach is
that it gives directly the higher derived structure on the moduli
space in question. We will focus on the case of sheaves on
projective varieties. We will examine the case of the Hilbert
scheme of points on a Calabi-Yau threefold in particular
detail.
Referências
- Deformation
theory via differential graded Lie algebras - Marco
Manetti
- Lectures on
deformations of complex manifolds - Marco Manetti
- Injective
resolutions of BG and derived moduli spaces of local systems -
M. Kapranov
- A functorial
construction of moduli of sheaves - Luis Álvarez-Cónsul,
Alastair King