Abstract
This paper is a continuation of [BG]. In that paper, for any smooth complex curve X and n > 1, we constructed a canonical completion of the configuration space of all ordered n-tuples of distinct points of X. The completion is called Resolution of Diagonals. There is a natural stratification of the resolution of diagonals with the set of strata being parametrized by certain graphs. The homology groups of the strata turn out to be closely related to free Lie algebras. That relation played a crucial role in [BG]. It was used there for describing jets of functions on moduli spaces of principal G-bundles, a higher order analogue of the Kodaira-Spencer isomorphism.
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Ginzburg, V. (1995). Resolution of Diagonals and Moduli Spaces. In: Dijkgraaf, R.H., Faber, C.F., van der Geer, G.B.M. (eds) The Moduli Space of Curves. Progress in Mathematics, vol 129. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4264-2_9
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DOI: https://doi.org/10.1007/978-1-4612-4264-2_9
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