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Formal Kuranishi Families and Period Maps
After the results regarding coalgebras and \(L_{\infty }\)...
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Equivariant Kuranishi family of complex compact manifolds
We prove that actions of complex reductive Lie groups on a complex compact manifold are locally extendable to its Kuranishi family. This can be seen...
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Thickening of a Kuranishi Structure
Let X be a paracompact metrizable space, and let \(\widehat {\mathcal U} = (\{\mathcal U_p\},\{\Phi _{pq}\})\) be a Kuranishi structure on it.
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Admissible Kuranishi Structures
In this chapter we introduce the notion of an admissible Kuranishi structure. For this purpose we introduce the notion of an admissible orbifold, an...
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Kuranishi Structures and Good Coordinate Systems
In this chapter we define the notions of a Kuranishi structure and of a good coordinate system. We also study embedding between them, which describes...
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Fiber Product of Kuranishi Structures
Before studying fiber products we consider direct products. Let X i, i = 1, 2 be separable metrizable spaces, Z i ⊆ X i compact subsets, and...
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Extension of a Kuranishi Structure and Its Perturbation from Boundary to Its Neighborhood
In Chap. 16 we formulated various versions of corner compatibility conditions. To prove the results stated in Chap. 16 (and which also appear...
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From Good Coordinate Systems to Kuranishi Structures and Back with CF-Perturbations
As we explained at the end of Chap. 4 , it is more canonical to define the notion of fiber products of spaces with Kuranishi structure than to...
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A Weil–Petersson Type Metric on the Space of Fano Kähler–Ricci Solitons
In this paper, we define a Weil–Petersson type metric on the space of (shrinking) Kähler–Ricci solitons and prove a necessary and sufficient...
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Construction of a linear K-system in Hamiltonian Floer theory
The notion of linear K-system was introduced by the present authors as an abstract model arising from the structure of compactified moduli spaces of...
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Lagrangian Floer Theory and Its Deformations An Introduction to Filtered Fukaya Category
A-infinity structure was introduced by Stasheff in the 1960s in his homotopy characterization of based loop space, which was the culmination of...
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Normal form of equivariant maps in infinite dimensions
Local normal form theorems for smooth equivariant maps between infinite-dimensional manifolds are established. These normal form results are new even...
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On the Teichmüller stack of compact quotients of \({\text {SL}}_2({\mathbb {C}})\)
This article aims to pursue and generalize, by using the global point of view offered by the stacks, the local study made by Ghys (J für die reine...
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Kuranishi Structures and Virtual Fundamental Chains
The package of Gromov’s pseudo-holomorphic curves is a major tool in global symplectic geometry and its applications, including mirror symmetry and...
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On deformations of Fano manifolds
In this paper, we provide new necessary and sufficient conditions for the existence of Kähler–Einstein metrics on small deformations of a Fano...
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Deformations of Dolbeault cohomology classes
In this paper, we establish a deformation theory for Dolbeault cohomology classes valued in holomorphic tensor bundles. We prove the extension...
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Some remarks about deformation theory and formality conjecture
Using the algebraic criterion proved by Bandiera, Manetti and Meazzini, we show the formality conjecture for universally gluable objects with...
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Deformations of Dolbeault cohomology classes for Lie algebra with complex structures
In this paper, we study deformations of complex structures on Lie algebras and its associated deformations of Dolbeault cohomology classes. A...
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Notations and Conventions
We use ‘hat’ such as \(\widehat {\mathcal U}\) , \(\widehat {f}\) , \(\widehat {\mathfrak S}\) , \(\widehat {h}\) for an...