Related papers: Variation of Hodge structure for generalized compl…
We consider compact K\"ahlerian manifolds $X$ of even dimension 4 or more, endowed with a log-symplectic holomorphic Poisson structure $\Pi$ which is sufficiently general, in a precise linear sense, with respect to its (normal-crossing)…
The main purpose of this paper is to lay the foundations of a general theory which encompasses the features of the classical Hough transform and extend them to general algebraic objects such as affine schemes. The main motivation comes from…
We define Hodge correlators for a compact Kahler manifold X. They are complex numbers which can be obtained by perturbative series expansion of a certain Feynman integral which we assign to X. We show that they define a functorial real…
We prove that if a compact K\"ahler Poisson manifold has a symplectic leaf with finite fundamental group, then after passing to a finite \'etale cover, it decomposes as the product of the universal cover of the leaf and some other Poisson…
Let $P$ be the image of a period map. We discuss progress towards a conjectural Hodge theoretic completion $\overline{P}$, an analogue of the Satake-Baily-Borel compactification in the classical case. The set $\overline{P}$ is defined and…
We adapt algorithms for resolving the singularities of complex algebraic varieties to prove that the natural map of homology theories from complex bordism to the bordism theory of complex derived orbifolds splits. In equivariant stable…
On a compact K\"{a}hler manifold $X$ with a holomorphic 2-form $\a$, there is an almost complex structure associated with $\a$. We show how this implies vanishing theorems for the Gromov-Witten invariants of $X$. This extends the approach,…
The goal is to verify the Hodge conjecture (and some related conjectures) for certain moduli spaces. It is shown that the (generalized) Hodge conjecture holds for the projective moduli spaces of vector bundles over an abelian or K3 surface…
We give a description of cyclic cohomology and its pairing with K-groups for 2-cocycle deformation of algebras graded over discrete groups. The proof relies on a realization of monodromy for the Gauss-Manin connection on periodic cyclic…
The Hodge conjecture is a major open problem in complex algebraic geometry. In this survey, we discuss the main cases where the conjecture is known, and also explain an approach by Griffiths-Green to solve the problem.
The infinitesimal period relation (also known as Griffiths' transversality) is the system of partial differential equations constraining variations of Hodge structure. This paper presents a study of the characteristic cohomology associated…
We discuss the variations of mixed Hodge structure for cohomology with compact support of quasi-projective simple normal crossing pairs. We show that they are graded polarizable admissible variations of mixed Hodge structure. Then we prove…
The main result is the identification of the orthogonal complement of the subalgebra of conformal vector field inside the algebra of all vector fields of a compact flat 2-manifold. As a fundamental tool, the complete Hodge decomposition for…
We study the weighted spectrum and vanishing cohomology for several classes of isolated hypersurface singularities, and how they contribute to the limiting mixed Hodge structure of a smoothing. Applications are given to several types of…
Recent discoveries make it possible to compute the K-theory of certain rings from their cyclic homology and certain versions of their cdh-cohomology. We extend the work of G. Corti\~nas et al. who calculated the K-theory of, in addition to…
We introduce conformal Courant algebroids, a mild generalization of Courant algebroids in which only a conformal structure rather than a bilinear form is assumed. We introduce exact conformal Courant algebroids and show they are classified…
We prove a generalisation of Bott's vanishing theorem for the full transverse frame holonomy groupoid of any transversely orientable foliated manifold. As a consequence we obtain a characteristic map encoding both primary and secondary…
We study the infinitesimal variation of Hodge structure associated with families of reduced algebraic curves with singularities. The analysis applies to curves beyond the nodal case and is not restricted to plane curves, encompassing curves…
We prove a general version of the homological perturbation lemma which works in the presence of curvature, and without the restriction to strong deformation retracts, building on work of Markl. A key observation is that the notion of strong…
Deformation theory is treated for locally notherian formal schemes (non necessarily smooth). The cotangent complex is defined in the derived category through the homology localization functor. The basic properties and results of a…