Construction of Maurer-Cartan elements over configuration spaces of curves
Abstract
For C a complex curve and n ≥ 1, a pair ($P$, $\Delta_P$) of a principal bundle $P$ with meromorphic flat connection over $C^n$ , holomorphic over the configuration space $C_n(C)$ of n points over $C$, was introduced in [En]. For any point ∞ ∈ C, we construct a trivialisation of the restriction of P to (C \ ∞)$^n$ and obtain a Maurer-Cartan element $J$ over $C_n$(C \ ∞) out of $\Delta_P$ , thus generalising a construction of Levin and Racinet when the genus of C is higher than one. We give explicit formulas for J as well as for $\Delta_P$. When n = 1, this construction gives rise to elements of Hain's space of second kind iterated integrals over C.
Domains
Algebraic Geometry [math.AG]
Origin : Files produced by the author(s)