Related papers: Iterated integrals on affine curves

In this paper we prove a tertiary index theorem which relates a spectral geometric and a homotopy theoretic invariant of an almost complex manifold with framed boundary. It is derived from the index theoretic and homotopy theoretic versions…

We obtain results on approximation of holomorphic maps by algebraic maps, jet transversality theorems for holomorphic and algebraic maps, and the homotopy principle for holomorphic submersions of Stein manifolds to certain algebraic…

We construct models for the motivic homotopy category based on simplicial functors from smooth schemes over a field to simplicial sets. These spaces are homotopy invariant and therefore one does not have to invert the affine line in order…

A simplicial analogy of Chen's iterated integral was introduced in another paper. However, its properties were hardly investigated in the paper. In particular, no mention is made of whether it coincides with Chen's iterated integral as a…

Starting from a result of Stewart, Tijdeman and Ruzsa on iterated difference sequences, we introduce the notion of iterated compositions of linear operations. We prove a general result on the stability of such compositions (with bounded…

The dimensions of the graded quotients of the cohomology of a plane curve complement with respect to the Hodge filtration are described in terms of simple geometrical invariants. The case of curves with ordinary singularities is discussed…

We study scalar one-loop amplitudes in massive $\phi^3$-theory within causal loop-tree duality. We derive a recurrence relation for the integrand of the amplitude. The integrand is by construction free of spurious singularities on…

We prove that affine invariant manifolds in strata of flat surfaces are algebraic varieties. The result is deduced from a generalization of a theorem of M\"oller. Namely, we prove that the image of a certain twisted Abel-Jacobi map lands in…

We study the symmetry properties of autonomous integrating factors from an algebraic point of view. The symmetries are delineated for the resulting integrals treated as equations and symmetries of the integrals treated as functions or…

We develop the theory of fractal homeomorphisms generated from pairs of overlapping affine iterated function systems.

We extend the theory of Interacting Hopf algebras with an order primitive, and give a sound and complete axiomatisation of the prop of polyhedral cones. Next, we axiomatise an affine extension and prove soundness and completeness for the…

We deduce from the work of Chen, that the restriction morphism from closed free iterated integrals to closed iterated integrals on loops is onto. We use this to show that the module of higher order invariants of smooth functions is…

We study algebraic and geometric properties of metric spaces endowed with dilatation structures, which are emergent during the passage through smaller and smaller scales. In the limit we obtain a generalization of metric affine geometry,…

We study projective completions of affine algebraic varieties induced by filtrations on their coordinate rings. In particular, we study the effect of the 'multiplicative' property of filtrations on the corresponding completions and…

Symplectic invariants introduced in math-ph/0702045 can be computed for an arbitrary spectral curve. For some examples of spectral curves, those invariants can solve loop equations of matrix integrals, and many problems of enumerative…

Classification of curves up to affine transformation in a finite dimensional space was studied by some different methods. In this paper, we achieve the exact formulas of affine invariants via the equivalence problem and in the view of…

The paper discusses the relationships between electrical and affine differential geometry quantities, establishing a link between frequency and time derivatives of voltage, through the utilization of affine geometric invariants. Based on…

In this note we study the homotopy type of the complement of a plane projective curve of fiber-type. Roughly speaking, a curve of fiber-type is a finite union of fibers of a pencil. Under some restrictions, a full description of their…

Modular graph forms are a class of non-holomorphic modular forms that arise in the low-energy expansion of genus-one closed string amplitudes. In this work, we introduce a systematic procedure to convert lattice-sum representations of…

The geometry of the moduli space of stable spin curves is studied, with emphasis on its combinatorial properties. In this context, the standard graph theoretic framework is not just a book-keeping device: some purely combinatorial results…