Related papers: Deformations of canonical singularities
We develop some basic facts on deformations of exterior differential ideals on a smooth complex algebraic variety. With these tools we study deformations of several types of differential ideals, leading to several irreducible components of…
The classical Cartan's structural equations show in a compact way the relation between a connection and its curvature, and reveals their geometric interpretation in terms of moving frames. In order to study the mathematical properties of…
Via elementary examples it is demonstrated that the singularities of classical physics (sampled by the Big Bang in cosmology) need not necessarily get smeared out after quantization. It is proposed that the role of quantum singularities can…
The action of the idempotent deformations on finite groups is discussed. This action is described in terms of the homological properties of groups. The orbits of finite simple groups are determined.
In this paper we introduce the notion of deformation cohomology for singular foliations and related objects (namely integrable differential forms and Nambu structures), and study it in the local case, i.e., in the neighborhood of a point.
The main theorem has been slightly generalized to include a larger class of symbols.
Birational Calabi-Yau threefolds in the same deformation family provide a `weak' counterexample to the global Torelli problem, as long as they are not isomorphic. In this paper, it is shown that deformations of certain desingularized…
Versal deformation of a matrix A is a normal form to which all matrices A + E, close to A, can be reduced by similarity transformation smoothly depending on the entries of A + E. In this paper we discuss versal deformations and their use in…
In this paper we obtain 32 canonical forms for 3D piecewise smooth vector fields presenting the so called cusp-fold singularity. All these canonical forms are topologically distinct and collect the main topological aspects of the…
We study functions on isolated singularities and prove some results of type Milnor number = Tjurina number. We use them to endow the base space of their miniversal deformation with the structure of F-manifold.
In this paper, we prove a result related to the deformation of complex submanifolds, modifying a result of Kodaira (Ann. Math, 75(1), 146-162, 1962).
We look at the decomposition of the compactified jacobian of a singular curve into components and discuss some examples.
For a normal subvariety $V$ of ${\bf C}^n$ with a good ${\bf C}^*$-action we give a simple characterization for when it has only log canonical, log terminal or rational singularities. Moreover we are able to give formulas for the…
Short survey about small eigenvalues of the Hodge Laplacian under bounded curvature collapsing.
We classify smooth Fano threefolds that admit degenerations to toric Fano threefolds with ordinary double points.
We study the structure of generalized Baumslag-Solitar groups from the point of view of their (usually non-unique) splittings as fundamental groups of graphs of infinite cyclic groups. We find and characterize certain decompositions of…
By developing a suitable version of the circle method, we show that the space of degree $e$ rational curves on a smooth hypersurface of degree $d$ has only canonical singularities provided its dimension is sufficiently large with respect to…
We refute a recent claim in the literature of a "new" quantum deformation of GL(2).
Extending the work of G. Sz\'ekelyhidi and T. Br\"onnle to Sasakian manifolds we prove that a small deformation of the complex structure of the cone of a constant scalar curvature Sasakian manifold admits a constant scalar curvature…
An I-surface $S$ is an algebraic surface of general type with $K_S^2 = 1$ and $p_g(S) = 2$. Recent research has centered on trying to give an explicit description of the KSBA compactification of the moduli space of these surfaces. The…