Handbook of Geometry and Topology of Singularities II, 1st ed. 2021

Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways.

The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Preface.- Contents.- Chapter 1 The Analytic Classificatio of Irreducible Plane Curve Singularities.- Chapter 2 Plane algebraic curves with prescribed singularities.- Chapter 3 Limit of tangents on complex surfaces.- Chapter 4 Algebro-geometric equisingularity of Zariski.- Chapter 5 Intersection homology.- Chapter 6 Milnor’s fibratio theorem for real and complex singularities.- Chapter 7 Lê Cycles and Numbers of hypersurface singularities.- Chapter 8 Introduction to mixed hypersurface singularity.  - Chapter 9 From Singularities to Polyhedral Products.- Chapter 10 Complements to ample divisors and Singularities.- Index.

José Luis Cisneros-Molina (PhD, University of Warwick 1999) is a full-time researcher at the Mathematics Institute of the National Autonomous University of Mexico. His research interests are in Algebraic and Differential Topology, Differential Geometry and Singularity Theory, with a particular focus on generalizations of Milnor Fibrations for complex and real analytic maps.

Dũng Tráng Lê (PhD, University of Paris 1969) is an Emeritus Professor at Aix-Marseille University. Previously he was Professor at the Universities of Paris VII (1975—1999)  and Marseille, and was head of Mathematics at the ICTP at Trieste. One of the founders of modern Singularity Theory, he has made numerous contributions to morsification, the topology of complex singularities, polar varieties, carousels, among other topics.

José Seade (DPhil, University of Oxford 1980) is a full-time researcher at the Mathematics Institute of the National Autonomous University of Mexico. His research is in the theory of indices of vector fields and Chern classes for singular varieties, with applications to foliations, and Milnor’s fibration theorem for analytic maps. In 2007 he was awarded the Ferran Sunyer i Ballaguer prize.

Presents in-depth and accessible surveys of topics in singularity theory, including their interrelationships and connections with other subjects

Ideal for graduate students and researchers in general who want to learn about this active field, and as a reference for specialists

Emphasizes clarity and quality of exposition rather than technical details

Encourages readers to go deeper into the subject by offering illuminating insights and useful bibliographies