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