120 citations · 669 across the 39 of their papers we have counts for
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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…
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…
Rescalability of integrable mixed twistor -modules
Takuro Mochizuki
We study the rescalability of integrable mixed twistor -modules. We prove some basic functoriality of the rescalability and the associated irregular Hodge filtration. We also ob…
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…
Twistor property of GKZ-hypergeometric systems
Takuro Mochizuki
We study the mixed twistor D-modules associated to meromorphic functions. In particular, we describe their push-forward and specialization under some situations. We apply the resul…
A twistor approach to the Kontsevich complexes
Takuro Mochizuki
This is a note to revisit interesting results of H. Esnault, C. Sabbah, M. Saito and J.-D. Yu on the Kontsevich complexes from the viewpoint of mixed twistor D-modules. We explicit…
Holonomic D-modules with Betti structure
Takuro Mochizuki
We define the notion of Betti structure for holonomic D-modules which are not necessarily regular singular. We establish the fundamental functorial properties. We also give auxilia…
Good formal structure for meromorphic flat connections on smooth projective surfaces
Takuro Mochizuki
We prove the algebraic version of a conjecture of C. Sabbah on the existence of the good formal structure for meromorphic flat connections on surfaces after some blow up.
The structure of the cohomology ring of the filt schemes
Takuro Mochizuki
Let be a smooth projective curve over the complex number field $\cnum$. We investigate the structure of the cohomology ring of the quot schemes $\Quot(r,n)$, i.e., the moduli s…
The geometry of the parabolic Hilbert schemes
Takuro Mochizuki
We discuss the parabolic Hilbert scheme of points on smooth surface, which is an interesting generalization of Hilbert scheme of points on surface. Some of the studies by Ellingsru…
A theory of the invariants obtained from the moduli stacks of stable objects on a smooth polarized surface
Takuro Mochizuki
Let be a smooth polarized algebraic surface over the compex number field. We discuss the invariants obtained from the moduli stacks of semistable sheaves of arbitrary ranks on…