相关论文: Jump of Milnor numbers
We give a simple way to study the isotypical components of the homology of simplicial complexes with actions of finite groups, and use it for Milnor fibers of ICIS. We study the homology of images of mappings $f_t$ that arise as…
The Milnor number of an isolated hypersurface singularity, defined as the codimension $\mu(f)$ of the ideal generated by the partial derivatives of a power series $f$ whose zeros represent locally the hypersurface, is an important…
The first part of Hilbert's sixteenth problem deals with the classification of the isotopy types realizable by real plane algebraic curves of a given degree $m$. For $m = 9$, the classification of the $M$-curves is still wide open. Let…
The integral variation map and algebraic monodromy of isolated plane curve singularities are important homological invariants of the singularity which are still far from being completely understood. This work provides effective ways of…
In this paper we study the geometry of the Severi varieties parametrizing curves on the rational ruled surface $\fn$. We compute the number of such curves through the appropriate number of fixed general points on $\fn$, and the number of…
In this paper, we give a simple description of the deformations of a map between two smooth curves with partially prescribed branching, in the cases that both curves are fixed, and that the source is allowed to vary. Both descriptions work…
In this paper we derive congruences expressing Bell numbers and derangement numbers in terms of each other modulo any prime.
The aim of this paper is to develop on the 1-jet space J^1(R, M^n) the Finsler-like geometry (in the sense of distinguished (d-) connection, d-torsions, d-curvatures and some gravitational-like and electromagnetic-like geometrical models)…
We present a quantum deformation theory of the Airy curve and use it to establish a version of mirror symmetry of a point.
We study Gromov's problem concerning minimal normal curvature immersions in the unit ball. In particular, we determine the minimal possible value of the normal curvature of an $S^n\times S^1$. We also prove a differentiable sphere theorem…
We introduce several sufficient conditions to guarantee the existence of the Milnor vector field for new classes of singularities of map germs. This special vector field is related with the equivalence problem of the Milnor fibrations for…
Curves of maximal slope are a reference gradient-evolution notion in metric spaces and arise as variational formulation of a vast class of nonlinear diffusion equations. Existence theories for curves of maximal slope are often based on…
In this paper we investigate how germs of real functions can change under deformation. In particular we look at deformations of germs of isolated singularities from R_n to R_k (n >= k) and the relation with there natural stratification in…
For a complex analytic map f from n-space to p-space with n<p and with an isolated instability at the origin, the disentanglement of f is a local stabilization of f that is analogous to the Milnor fibre for functions. For mono-germs it is…
We introduce a "deformation" of plumbing. We also define a structure of data used in a calculation by computer aid of the crosscap numbers of alternating knots.
We present a complete set of criteria for determining A-types of plane-to-plane map-germs of corank one with A-codimension <7, which provides a new insight into the A-classification theory from the viewpoint of recognition problem. As an…
Assume that $f:(\mathbb{C}^n,0) \to (\mathbb{C},0)$ is an analytic function germ at the origin with only isolated singularity. Let $\mu$ and $\tau$ be the corresponding Milnor and Tjurina numbers. We show that $\dfrac{\mu}{\tau} \leq n$. As…
We study the a-numbers and p-ranks of Kummer covers of the projective line, and we give bounds for these numbers.
In this paper we study the integrals of fractional parts of given functions, and develop some new tools to understand the behaviour of prime differences. We demonstrate how simply some seemingly difficult conjectures related to prime…
We investigate splitting-type variational problems with some linear growth conditions. For balanced solutions of the associated Euler-Lagrange equation we receive a result analogous to Bernstein's theorem on non-parametric minimal surfaces.…