This paper contains a survey of research on critical points of smooth functions and their
bifurcations. We indicate applications to the theory of Lagrangian singularities (caustics) …

Introduction Let Pe C [z,---, z,] with P (0)= 0. Assume that 0= C" is a critical point of P. Denote
B the open ball in C" with center 0 and radius s> 0. There exists n> 0 such that 0<| t|< n …

Singularity theory is not a field in itself, but rather an application of algebraic geometry,
analytic geometry and differential analysis. The adjective'singular'in the title refers here to …

Abstract Contents Introduction Some definitions § 1. Picard-Lefschetz theory § 2. The
monodromy group and variation operator of a singularity § 3. The intersection matrices of …

From the reviews:"... My general impression is of a particularly nice book, with a well-
balanced bibliography, recommended!" Mededelingen van Het Wiskundig Genootschap …

We study the singularity category of the triangle singularity f= xa+ yb+ zc, or S= k [x, y, z]/(f),
attached to the weighted projective line X, given by the weight triple (a, b, c), by investigating …

AMS :: Bulletin of the American Mathematical Society Skip to Main Content American
Mathematical Society American Mathematical Society MathSciNet Bookstore Publications …

The systematic study of rational surfaces $ Y $ with an anticanonical cycle $ D $ dates back
to a fundamental paper of Looijenga in 1981. Recently, Gross, Hacking and Keel have …

We show a surprising link between singularity theory and the invariant subspace problem of
nilpotent operators as recently studied by CM Ringel and M. Schmidmeier, a problem with a …

The Milnor fibre of any isolated hypersurface singularity contains many exact Lagrangian
spheres: the vanishing cycles associated to a Morsification of the singularity. Moreover, for …