7 papers
A generalization of Barannikov-Kontsevich theorem
Takuro Mochizuki
We study the twisted de Rham complex associated with a holomorphic function on a Kähler manifold whose critical point set is compact. We prove the -degeneration of the Hodge-…
Specialized Simpson's main estimates for cyclic harmonic -bundles
Takuro Mochizuki
We study a generalization of specialized Simpson's main estimate in the context of cyclic harmonic -bundles induced by split automorphisms. We apply it to the classification of…
Algebraic integrable connections with bounded irregularity
Takuro Mochizuki
We study the boundedness of families of algebraic flat connections with bounded irregularity. As an application, we study the boundedness of families of holonomic -modules with…
Asymptotic behaviour of the Hitchin metric on the moduli space of Higgs bundles
Takuro Mochizuki
The moduli space of stable Higgs bundles of degree is equipped with the hyperkähler metric, called the Hitchin metric. On the locus where the spectral curves are smooth, there…
Stokes shells and Fourier transforms
Takuro Mochizuki
Algebraic holonomic -modules on a complex line are classified by the associated topological data consisting of local systems with Stokes structure and the nearby and v…
Semi-flat metrics of the moduli spaces of Higgs bundles in the non-zero degree case
Takuro Mochizuki
We study horizontal deformations of a Higgs bundle whose spectral curve is smooth. It allows us to define a natural integrable connection of the Hitchin fibration on the locus wher…