The Bogomolov-Tian-Todorov theorem ([10] and [12]) states that a non-singular n-fold X with c 1 (X) = 0 has unobstructed deformation theory, i.e. the moduli space of X is non-singular. This theorem was reproven using algebraic methods by Ran in [7]. Since then, it has been proven for Calabi-Yau n-folds with various mild forms of isolated singularities: ordinary double points by Kawamata [5] and...

It has long been known that every quasi-homogeneous normal complex surface singularity with Q–homology sphere link has universal abelian cover a Brieskorn complete intersection singularity. We describe a broad generalization: First, one has a class of complete intersection normal complex surface singularities called “splice type singularities,” which generalize Brieskorn complete intersections....

This article recounts the rather wonderful interaction of topology and singularity theory which began to flower in the 1960’s with the work of Hirzebruch, Brieskorn, Milnor and others. This interaction can be traced back to the work of Klein, Lefschetz and Picard, and also to the work of knot theorists at the beginning of this century. It continues to the present day, flourishing and expanding ...

Present knowledge about the nature of spacetime singularities in the context of classical general relativity is surveyed. The status of the BKL picture of cosmological singularities and its relevance to the cosmic censorship hypothesis are discussed. It is shown how insights on cosmic censorship also arise in connection with the idea of weak null singularities inside black holes. Other topics c...

It is now well-established that a variety of singularities can be characterized and observed in optical wavefields. It is also known that these phase singularities, polarization singularities and coherence singularities are physically related, but the exact nature of their relationship is still somewhat unclear. We show how a Young-type three-pinhole interference experiment can be used to creat...

These proceedings are based on lectures delivered at the “RTN Winter School on Strings, Supergravity and Gauge Theories”, CERN, January 16 January 20, 2006. The school was mainly aimed at Ph.D. students and young postdocs. The lectures start with a brief introduction to spacetime singularities and the string theory resolution of certain static singularities. Then they discuss attempts to resolv...

This paper is devoted to some fundumental calculation on 2-dimensional smoothable semi-log-terminal singularities. If we study minimal or canonical models of one parameter degeneration of algebraic surfaces, we must treat singularities that appear in the central fiber. Smoothable semi-log-terminal singularities are the singularities of the central fiber of the minimal model of degeneration, and...

this paper is devoted to the proof of the unique solvability ofthe inverse problems for second-order differential operators withregular singularities. it is shown that the potential functioncan be determined from spectral data, also we prove a uniquenesstheorem in the inverse problem.