Normal Surface Singularities

András Némethi studied algebraic geometry with Lucian Badescu at Bucharest and then spent 14 years at Ohio State University. He now works at the Alfréd Rényi Institute of Mathematics and at the Eötvös Loránd University in Budapest. A leading researcher in the theory of complex singularities and their connections with low-dimensional topology, he co-authored the book Milnor Fiber Boundary of a Non-Isolated Surface Singularity, and has authored some 130 research articles, many of them with various collaborators. His honors include an invited address to the International Congress of Mathematicians in 2018. He has built new bridges between analytic and topological invariants (for instance, between the geometric genus and the Seiberg–Witten invariant of the link), proved and formulated several conjectures, and introduced new mathematical objects, such as (topological and analytic) lattice cohomologies and graded roots.

• 1 Introduction.- 2 Resolution of Surface Singularities.- 3 The Link.- 4 Coverings.- 5 Examples.- 6 Invariants Associated With a Resolution.- 7 The Artin–Laufer Program.- 8  Multivariable Divisorial Filtration.- 9 Topological Invariants. The Seiberg–Witten Invariant.- 10 Ehrhart Theory and the Seiberg–Witten Invariant.- 11 Lattice Cohomology.- 12 Appendix. Complex Analytic Spaces.- References.- Index.

“The book serves its main purpose in a perfect way, and will be a very useful guide or handbook for readers working in algebraic geometry, complex analytic geometry, and algebraic topology. Experts in this field will also enjoy the various topics and discover new perspectives. It is self-contained regarding the main materials and provides detailed explanations of techniques and related topics. For these reasons, this book is a very useful for young researchers as well.” (Tomohiro Okuma, zbMATH 1523.14001, 2023)