Related papers: Formal Abel-Jacobi maps

We construct an Abel-Jacobi type map on the homologically trivial part of Lawson homology groups. It generalizes the Abel-Jacobi map constructed by Griffiths. By using a result of H. Clemens, we give some examples of smooth projective…

For a complex projective manifold, Walker has defined a regular homomorphism lifting Griffiths' Abel-Jacobi map on algebraically trivial cycle classes to a complex abelian variety, which admits a finite homomorphism to the Griffiths…

To a homotopy algebra one may associate its deformation complex, which is naturally a differential graded Lie algebra. We show that infinity quasi-isomorphic homotopy algebras have L-infinity quasi-isomorphic deformation complexes by an…

As an application of the theory of Lawson homology and morphic cohomology, Walker proved that the Abel-Jacobi map factors through another regular homomorphism. In this note, we give a direct proof of the theorem.

This work explores the deformation theory of algebraic structures in a very general setting. These structures include commutative, associative algebras, Lie algebras, and the infinity versions of these structures, the strongly homotopy…

We study the higher Abel-Jacobi invariant defined recently by M. Green. We first construct a counterexample to the injectivity of Green's higher Abel-Jacobi map. On the other hand, we prove that the higher Abel-Jacobi map governs Mumford's…

In this paper we study cohomology and deformations of Jacobi-Jordan algebras. We develop their formal deformation theory. In particular, we introduce a method to construct a versal deformation for a given Jacobi-Jordan algebra, which can…

We prove and generalize an observation of Green and Griffiths on the infinitesimal form of the Abel-Jacobi map. As an application, we prove that the infinitesimal form of a conjecture by Griffiths and Harris is true.

We construct the deformation functor associated with a pair of morphisms of differential graded Lie algebras, and use it to study infinitesimal deformations of holomorphic maps of compact complex manifolds. In particular, using L-infinity…

In this article, we study the infinitemisal invariant of the relative higher Abel Jacobi map of a smooth open morphism. We give a generalization of a theorem of Voisin to open varieties and higher Chow groups and as a corollary a non…

Using the BV-formalism of mathematical physics an explicit construction for the minimal model of a quantum L-infinity-algebra is given as a formal super integral. The approach taken herein to these formal integrals is axiomatic; they can be…

We discuss the appearance of Jacobi automorphic forms in the theory of superconformal vertex algebras, explaining it by way of supercurves and formal geometry. We touch on related topics such as Ramanujan's differential equations for…

We introduce a notion of elliptic differential graded Lie algebra. The class of elliptic algebras contains such examples as the algebra of differential forms with values in endomorphisms of a flat vector bundle over a compact manifold, etc.…

Diffieties formalize geometrically the concept of differential equations. We introduce and study Hamilton-Jacobi diffieties. They are finite dimensional subdiffieties of a given diffiety and appear to play a special role in the field…

We investigate questions of an arithmetic nature related to the Abel-Jacobi map. We give a criterion for the zero locus of a normal function to be defined over a number field, and we give some comparison theorems with the Abel-Jacobi map…

We construct the deformation functor associated to a couple of morphisms of differential graded Lie algebras, and use it to study the infinitesimal deformations of a holomorphic map of compact complex manifolds. In particular, in the case…

Let $C$ be a smooth non rational projective curve over the complex field $\mathbb{C}$. If $A$ is an abelian subvariety of the Jacobian $J(C)$, we consider the Abel-Prym map $\varphi_A : C \rightarrow A$ defined as the composition of the…

We study the differential graded Lie algebra of endomorphisms of the Koszul resolution of a regular sequence on a unitary commutative $K$-algebra $R$ and we prove that it is homotopy abelian over $K$, while it is generally not formal over…

We discuss an Abel-Jacobi invariant for algebraic cobordism cycles whose image in topological cobordism vanishes. The existence of this invariant follows by abstract arguments from the construction of Hodge filtered cohomology theories in…

We show how the Abel-Jacobi map provides all the principal properties of an ample family of integrable mechanical systems associated to hyperelliptic curves. We prove that derivative of the Abel-Jacobi map is just the St\"{a}ckel matrix,…