Related papers: Moduli of log mixed Hodge structures

We construct bordifications of the moduli spaces of tropical curves and of tropical abelian varieties, and show that the tropical Torelli map extends to their bordifications. We prove that the classical bi-invariant differential forms…

We continue our work on variations of graded-polarized mixed Hodge structures by defining analogs of the harmonic metric equations for filtered bundles and proving a precise analog of Schmid's Nilpotent Orbit Theorem for 1-parameter…

Multi-scale differentials were constructed by M.~Bainbridge, D.~Chen, Q.~Gendron, S.~Grushevsky, and M.~M\"oller, from the viewpoint of flat and complex geometry, for the purpose of compactifying moduli spaces of curves together with a…

We extend some of the results obtained for subvarieties of the moduli stack of canonically polarized manifolds in "Base spaces of non-isotrivial families of smooth minimal models" (math.AG/0103122) to moduli of polarized minimal models of…

We describe the moduli spaces of morphisms between polarized complex abelian varieties. The discrete invariants, derived from a Poincare' decomposition of morphisms, are the types of polarizations and of lattice homomorphisms occurring in…

Given a variation of Hodge structures on a quasi-projective base $S$, whose generic Mumford-Tate group is non-product, we prove that the (countable) union of positive components of the Hodge locus is either an algebraic subvariety of $S$,…

We prove a formality theorem for algebraic objects internal to smooth complex varieties that are not compact but whose mixed Hodge structure has a certain purity property.

We connect the homotopy type of simplicial moduli spaces of algebraic structures to the cohomology of their deformation complexes. Then we prove that under several assumptions, mapping spaces of algebras over a monad in an appropriate…

In this paper, we study moduli spaces of sextic curves with simple singularities. Through period maps of K3 surfaces with ADE singularities, we prove that such moduli spaces admit algebraic open embeddings into arithmetic quotients of type…

We describe some results on moduli space of logarithmic connections equipped with framings on a $n$-pointed compact Riemann surface.

This is a survey of vanishing and positivity theorems for Hodge modules, and their recent applications to birational and complex geometry, expanding on my lecture at the 2015 AMS Summer Institute.

Let $(X,\mathcal{O}_X(1))$ be a polarized smooth projective variety over the complex numbers. Fix $\mathcal{D}\in \mathrm{coh}(X)$ and a nonnegative rational polynomial $\delta$. Using GIT we contruct a coarse moduli space for…

Following our previous work, we develop an algorithm to compute a presentation of the fundamental group of certain partial compactifications of the complement of a complex arrangement of lines in the projective plane. It applies, in…

We show that the Fourier-Laplace transform of a regular holonomic module over the Weyl algebra of one variable, which generically underlies a variation of polarized Hodge structure, underlies itself an integrable variation of polarized…

In 1969, P. Deligne and D. Mumford compactified the moduli space of curves. Their compactification is a projective algebraic variety, and as such, it has an underlying analytic structure. Alternatively, the quotient of the augmented…

This article constructs Von Neumann invariants for constructible complexes and coherent D-modules on compact complex manifolds, generalizing the work of the author on coherent L 2-cohomology. We formulate a conjectural generalization of…

An important problem in the representation theory of affine and toroidal Lie algebras is to classify all possible irreducible integrable modules with finite dimensional weight spaces. Recently the irreducible integrable modules having…

To advance our log Hodge theory, we introduce log real analytic functions and log $C^{\infty}$ functions, define how to integrate them, and prove the log Poincar\'e lemma. We give better understandings of the degeneration of Hodge…

In this paper the authors consider a certain toroidal compactification of the moduli space of degenerations of (1,p)-polarized abelian surfaces with (canonical) level structure. Using Hodge theory we give a proof that a degenerate abelian…

We prove that a variation of mixed Hodge structure is embedded in a logarithmic variation of pure Hodge structure, and a generalized version of this result. These results suggest some simple construction of the category of mixed motives by…