Add to ORKGThis thesis contains two parts. In the first part, we will give the Deligne 1-motives up to isogeny corresponding to the Q-limit mixed Hodge structures of semi-stable degenerations of curves, using logarithmic structures and Steenbrink’s cohomological mixed Hodge complexes associated to semi-stable degenerations of curves. In the second part, we study the nonableian Hodge theory for nodal curves, construct a “Dolbeault moduli spaces” MDol(X,m) for Higgs bundles on nodal curves, and give the formality theorem for local systems and Higgs bundles on nodal curves. We also give some discussions on the Hitchin fibration of MDol(X,m) and the mixed Hodge structure on C∗-fixed points in MDol(X,m)
In this thesis, we studied the Hodge theory and deformation theory of nodal surfaces. We showed that...
This article is a generalization of the author's work [U] to the case of several variables. We first...
The mixed Hodge structure on the low degree cohomology of the moduli space of vector bundles on a cu...
This thesis contains two parts. In the first part, we will give the Deligne 1-motives up to isogeny ...
This thesis contains two parts. In the first part, we will give the Deligne 1-motives up to isogeny ...
In this thesis we explore variations of mixed Hodge structures, both locally and asymptotically. Fir...
In this article, we prove the Hodge conjecture for a desingularization of the moduli space of rank 2...
In this article, we prove the Hodge conjecture for a desingularization of the moduli space of rank 2...
In this thesis, we studied the Hodge theory and deformation theory of nodal surfaces. We showed th...
Abstract. Text of talk given at the Institut Henri Poincare ́ January 17th 2012, during program on s...
In ordinary Hodge theory for a compact kahler manifold, one can look at the Gauss-Manin connection a...
This thesis is concerned with the study of the geometry and derived categories associated to the mod...
In ordinary Hodge theory for a compact kahler manifold, one can look at the Gauss-Manin connection a...
Teichmüller curves are geodesic discs in Teichmüller space that project to an algebraic curve in t...
In ordinary Hodge theory for a compact kahler manifold, one can look at the Gauss-Manin connection a...
In this thesis, we studied the Hodge theory and deformation theory of nodal surfaces. We showed that...
This article is a generalization of the author's work [U] to the case of several variables. We first...
The mixed Hodge structure on the low degree cohomology of the moduli space of vector bundles on a cu...
This thesis contains two parts. In the first part, we will give the Deligne 1-motives up to isogeny ...
This thesis contains two parts. In the first part, we will give the Deligne 1-motives up to isogeny ...
In this thesis we explore variations of mixed Hodge structures, both locally and asymptotically. Fir...
In this article, we prove the Hodge conjecture for a desingularization of the moduli space of rank 2...
In this article, we prove the Hodge conjecture for a desingularization of the moduli space of rank 2...
In this thesis, we studied the Hodge theory and deformation theory of nodal surfaces. We showed th...
Abstract. Text of talk given at the Institut Henri Poincare ́ January 17th 2012, during program on s...
In ordinary Hodge theory for a compact kahler manifold, one can look at the Gauss-Manin connection a...
This thesis is concerned with the study of the geometry and derived categories associated to the mod...
In ordinary Hodge theory for a compact kahler manifold, one can look at the Gauss-Manin connection a...
Teichmüller curves are geodesic discs in Teichmüller space that project to an algebraic curve in t...
In ordinary Hodge theory for a compact kahler manifold, one can look at the Gauss-Manin connection a...
In this thesis, we studied the Hodge theory and deformation theory of nodal surfaces. We showed that...
This article is a generalization of the author's work [U] to the case of several variables. We first...
The mixed Hodge structure on the low degree cohomology of the moduli space of vector bundles on a cu...