Related papers: Kuranishi Spaces of Meromorphic Connections
A Kuranishi space is a topological space with a Kuranishi structure, defined by Fukaya and Ono. Kuranishi structures occur naturally on moduli spaces of J-holomorphic curves in symplectic geometry. This paper is a brief introduction to the…
A Kuranishi space is a topological space with a Kuranishi structure, defined by Fukaya and Ono. Kuranishi structures occur naturally on moduli spaces of J-holomorphic curves in symplectic geometry. Let Y be an orbifold and R a commutative…
We describe deformations of vector bundles on surfaces that are a product of two smooth projective curves. We explicitly describe the Kuranishi map around unstable vector bundles and compare the homologies of the Kuranishi spaces of stable…
Cohesive modules give a dg-enhancement of the bounded derived category of coherent sheaves on a complex manifold via superconnections. In this paper we discuss the deformation theory of cohesive modules on compact complex manifolds. This…
'Kuranishi spaces' were introduced in the work of Fukaya, Oh, Ohta and Ono in symplectic geometry (see e.g. arXiv:1106.4882), as the geometric structure on moduli spaces of $J$-holomorphic curves. An alternative to Kuranishi spaces is the…
This is the second of a series of two articles in which we provide detailed and self-contained account of the construction of a system of Kuranishi structures on the moduli spaces of pseudo holomorphic disks. Using the notion of obstruction…
We construct universal local deformations (Kuranishi families) for pairs consisting of a compact complex curve and a meromorphic 1-form. Each pair is assumed to be locally planar, a condition which in particular forces the periods of the…
We show that the deformation space of complex parallelisable nilmanifolds can be described by polynomial equations but is almost never smooth. This is remarkable since these manifolds have trivial canonical bundle and are holomorphic…
This is a comment on the Kuranishi method of constructing analytic deformation spaces. It is based on a simple observation that the Kuranishi map can always be inverted in the category of $L_{\infty}$-algebras. The $L_{\infty}$-structure…
Motivated by the definition of homotopy $L_\infty$ spaces, we develop a new theory of Kuranishi manifolds, closely related to Joyce's recent theory. We prove that Kuranishi manifolds form a $2$-category with invertible $2$-morphisms, and…
Using homological perturbation theory, we develop a formal version of the miniversal deformation associated with a deformation problem controlled by a differential graded Lie algebra over a field of characteristic zero. Our approach…
Kuranishi's fundamental result (1962) associates to any compact complex manifold $X_0$ a finite-dimensional analytic space which has to be thought of as a local moduli space of complex structures close to $X_0$. In this paper, we give an…
We provide a sketch of the GIT construction of the moduli spaces for the three classes of connections: the class of meromorphic connections with fixed divisor of poles $D$ and its subclasses of integrable and integrable logarithmic…
This is a survey of the author's paper arXiv:1409.6908 and in-progress book. 'Kuranishi spaces' were introduced in the work of Fukaya, Oh, Ohta and Ono in symplectic geometry (see e.g. arXiv:1503.07631), as the geometric structure on moduli…
We describe the generalized Kuranishi spaces of solvmanifolds with left-invariant complex structures. By using such description, we study the stability of left-invariantness of deformed generalized complex structures and smoothness of…
We introduce $L_{\infty}$-Kuranishi spaces by associating, to each chart, $L_{\infty}[1]$-algebras defined on open neighborhoods of the zero points of the Kuranishi section. We show that these objects collectively form a category, which…
We determine the base space of the Kuranishi family of some complete intersection in the product of an abelian variety and a projective space. As a consequence we obtain new examples of obstructed irregular surfaces with ample canonical…
This article is the second part of the article we promised to write at the end of Section 1 of [FOOO15] (arXiv:1209.4410). (Part I appeared in [Part I] (arXiv:1503.07631).) We discuss the foundation of the virtual fundamental chain and…
This paper constructs a Kuranishi structure for the moduli stack of holomorphic curves in exploded manifolds. To avoid some technicalities of abstract Kuranishi structures, we embed our Kuranishi structure inside an ambient moduli stack of…
This is the first of two articles in which we provide detailed and self-contained account of the construction of a system of Kuranishi structures on the moduli spaces of pseudo holomorphic disks, using the exponential decay estimate given…