Related papers: Integrable deformations and degenerations of some …
Let f_0 be a plane curve singularity. We study the Minor numbers of singularities in deformations of f_0. We completely describe the set of these Milnor numbers for homogeneous singularities f_0 in the case of non-degenerate deformations…
This paper is the first arising from our project announced in math.AG/0211094, "Affine manifolds, log structures, and mirror symmetry." We aim to study mirror symmetry by studying the log structures of Illusie-Fontaine and Kato on…
This article is a summary of the author's unpublished Ph.D thesis. Its purpose is to generalise a construction by H. Cassens and P. Slodowy of the semiuniversal deformations of the simple singularities of type $A_r$, $D_r$, $E_6$, $E_7$ and…
This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…
Let $X\to\P^n$ be a $2n$-dimensional projective holomorphic symplectic manifold admitting a Lagrangian fibration over $\P^n$. Matsushita proved that the fibration can be deformed in a codimension one family in the moduli space…
A meromorphic connection on the tangent bundle of a Riemann surface induces a complex affine structure on the complement of the poles. Local models for Fuchsian singularities are already known. In this paper, we introduce a complete set of…
This paper uses noncommutative resolutions of non-Gorenstein singularities to construct classical deformation spaces, by recovering the Artin component of the deformation space of a cyclic surface singularity using only the quiver of the…
The new idea of flip invariance of action functionals in multidimensional lattices was recently highlighted as a key feature of discrete integrable systems. Flip invariance was proved for several particular cases of integrable…
We construct the deformation functor associated to a couple of morphisms of differential graded Lie algebras, and use it to study the infinitesimal deformations of a holomorphic map of compact complex manifolds. In particular, in the case…
In this paper, we consider the degenerate Frobenius-Euler polynomials and investigate some identities of these polynomials.
The standard generators of tridiagonal algebras, recently introduced by Terwilliger, are shown to generate a new (in)finite family of mutually commuting operators which extends the Dolan-Grady construction. The involution property relies on…
Mather and Yau showed that an isolated complex hypersurface singularity is completely determined by its moduli algebra. It is shown, for the simple elliptic singularities, how to construct continuous invariants from the moduli algebras and,…
We extend a classical fact about deformations of groups of units of commutative rings to $\mathbb{E}_{\infty}$-ring spectra, and we use this result to provide a map of spectra generalizing the ordinary logarithmic derivative induced by an…
We present the extended Kuranishi space for Kodaira surface as a non-trivial example to Kontsevich and Barannikov's extended deformation theory. We provide a non-trivial example of Hertling-Manin's weak Frobenius manifold. In addition, we…
In this note we extend to arbitrary dimensions a couple of results due respectively to Mattei-Moussu and to Camara-Scardua in dimension 2. We also provide examples of singular foliations having a Siegel-type singularity and answering in the…
A construction theorem for Frobenius manifolds with logarithmic poles is established. This is a generalization of a theorem of Hertling and Manin. As an application we prove a generalization of the reconstruction theorem of Kontsevich and…
The aim of this work is to discuss the concepts of degeneration, deformation and rigidity, and to apply them to the geometric study of the varieties of Hopf algebras. The main result is the description of the n-dimensional rigid Hopf…
For a general cubic fourfold, it was observed by Donagi and Markman that the relative intermediate Jacobian fibration associated to the family of its hyperplane sections carries a natural holomorphic symplectic form making the fibration…
We describe the construction of Frobenius manifold out of a cyclic (commutative) $BV_\infty$ algebra $(A,\Delta)$ under the assumption of a Hodge-to-de Rham degeneration property and the existence of a compatible homotopy retract of $A$…
It was suggested on several occasions by Deligne, Drinfeld and Kontsevich that all the moduli spaces arising in the classical problems of deformation theory should be extended to natural "derived" moduli spaces which are always smooth in an…