Formality of Kapranov's brackets in K\"ahler geometry via pre-Lie deformation theory

We recover some recent results by Dotsenko, Shadrin and Vallette on the Deligne groupoid of a pre-Lie algebra, showing that they follow naturally by a pre-Lie variant of the PBW Theorem. As an application, we show that Kapranov's $L_\infty$ algebra structure on the Dolbeault complex of a K\"ahler manifold is homotopy abelian and independent on the choice of K\"ahler metric up to an $L_\infty$ isomorphism, by making the trivializing homotopy and the $L_\infty$ isomorphism explicit.Comment: This is a new version of the old "Formality of Kapranov's brackets on pre-Lie algebras". To appear in Int. Math. Res. No

Land Distribution, Incentives and the Choice of Production Techniques in Nicaragua

Does the distribution of land rights affect the choice of contractible techniques? I present evidence suggesting that Nicaraguan farmers are more likely to grow effort-intensive crops on owned rather than on rented plots. I consider two theoretical arguments that illustrate why property rights might matter. In the first the farmer is subject to limited liability; in the second the owner cannot commit to output-contingent contracts. In both cases choices might be inefficient regardless of land distribution. The efficiency loss, however, is lower when the farmer owns the land. Further evidence suggests that, in this context, the inefficiency derives from lack of commitment.Agricultural productivity, asymmetric information, crop choice.

How to discretize the differential forms on the interval

We provide explicit quasi-isomorphisms between the following three algebraic structures associated to the unit interval: i) the commutative dg algebra of differential forms, ii) the non-commutative dg algebra of simplicial cochains and iii) the Whitney forms, equipped with a homotopy commutative and homotopy associative, i.e. $C_\infty$, algebra structure. Our main interest lies in a natural `discretization' $C_\infty$ quasi-isomorphism $\varphi$ from differential forms to Whitney forms. We establish a uniqueness result that implies that $\varphi$ coincides with the morphism from homotopy transfer, and obtain several explicit formulas for $\varphi$, all of which are related to the Magnus expansion. In particular, we recover combinatorial formulas for the Magnus expansion due to Mielnik and Pleba\'nski.Comment: 29 pages, extended abstract, typos fixe

Algebraic models of local period maps and Yukawa algebras

We describe some L-infinity model for the local period map of a compact Kaehler manifold. Applications include the study of deformations with associated variation of Hodge structure constrained by certain closed strata of the Grassmannian of the de Rham cohomology. As a byproduct we obtain an interpretation in the framework of deformation theory of the Yukawa coupling.Comment: to appear in Letters in Mathematical Physic