Algebraic Geometry / Moduli Seminar 

07/02/2011, 15:00 — 16:00 — Room P3, Mathematics Building, IST
Pietro Tortella, SISSA

Moduli spaces for Lie-algebroid connections

In a paper of '94 C. Simpson constructed moduli spaces for a large class of objects, namely semistable $\Lambda$-modules. Main examples of this include flat connections, Higgs bundles, connection along foliations and logaritmic connections. We shall show that Simpson's axioms for the algebra $\Lambda$ canonically associate to it a Lie algebroid and an element of the second cohomology of the algebroid, so that the objects that one get through Simpson's formalism are Lie algebroid connections whose curvature is controlled by the second cohomology class.