Related papers: A note on singularity of fibers of singular sets

The paper discusses some uniqueness sets for Fourier series.

We describe the singular fibers of a parabolic fibration $f:X\to Y$ whose moduli divisor $M_Y$ is numerically trivial and discriminant divisor $B_Y$ is zero.

In a family of curves, the Chern numbers of a singular fiber are the local contributions to the Chern numbers of the total space. We will give some inequalities between the Chern numbers of a singular fiber as well as their lower and upper…

We discuss the most general condition under which a singular local tube fibration exists. We give an application to composition of map germs.

I give various criteria for singularities to appear on geometric generic fibers of morphism between smooth schemes in positive characteristics. This involves local fundamental groups, jacobian ideals, projective dimension, tangent and…

We describe the construction of the slice fibration of a given one.

In this new version, we add the proof of the main theorem when the central fiber is not necessarily simple normal crossing. We also correct some typos.

We study the existence problem and the enumeration problem for sections of Serre fibrations over compact orientable surfaces. When the fundamental group of the fiber is finite, a complete solution is given in terms of 2-dimensional…

The paper contains a review on the general connection theory on differentiable fibre bundles. Particular attention is paid to (linear) connections on vector bundles. The (local) representations of connections in frames adapted to holonomic…

This is the abstract prepared for Workshop on Topology and Geometry (Zhang jiang, China, October 1994), and is a review of my recent works. What kinds of combinations of singularities can appear in small deformation fibers of a fixed…

In this note we provide a simple formula of general term of recurrent sequence.

Either fibered knots supporting the tight contact structure are unique in their smooth concordance class or there exists a fibered counterexample to the Slice-Ribbon Conjecture.

These notes give an exposition of Deligne's theorem on the existense of super fiber functor.

We establish a theory of singular Soergel bimodules which is a generalization of (a part of) Williamson's theory. We use a formulation of Soergel bimodules developed by the author.

This brief survey of some singularity invariants related to Milnor fibers should serve as a quick guide to references. We attempt to place things into a wide geometric context while leaving technicalities aside. We focus on relations among…

In the present paper we consider fibrations $f: S \ra B$ of an algebraic surface onto a curve $B$, with general fibre a curve of genus $g$. Our main results are: 1) A structure theorem for such fibrations in the case $g=2$ 2) A structure…

Essentials of sheaves are briefly presented, followed by related comments on presheaves, bundles, manifolds and singularities, aiming to point to their differences not only in their different formal mathematical structures, but also in the…

A new generalization of the classical separate algebraicity theorem is suggested and proved.

We describe a general method, originated by Ofer Gabber, for showing that a very general fiber in a family has certain properties. We illustrate this method with concrete examples taken from algebraic dynamics, the rationality problem for…

In this note some properties of the sum of element orders of a finite abelian group are studied.