Singularities and Their Interaction with Geometry and Low Dimensional Topology

The book is a collection of surveys and original research articles concentrating on new perspectives and research directions at the crossroads of algebraic geometry, topology, and singularity theory. The papers, written by leading researchers working on various topics of the above fields, are the outcome of the Némethi60: Geometry and Topology of Singularities conference held at the Alfréd Rényi Institute of Mathematics in Budapest, from May 27 to 31, 2019. Both the conference and this resulting volume are in honor of Professor András Némethi, on the occasion of his 60th birthday, whose work plays a decisive and influential role in the interactions between the above fields.

The book should serve as a valuable resource for graduate students and researchers to deepen the new perspectives, methods, and connections between geometry and topology regarding singularities.

Inhalt

Versality, bounds of global Tjurina numbers and logarithmic vector fields along hypersurfaces with isolated singularities.- On ideal filtrations for Newton nondegenerate surface singularities.- Young walls and equivariant Hilbert schemes of points in type D.- Real Seifert forms, Hodge numbers and Blanchfield pairings.- h-deformed Schubert calculus in equivariant cohomology, K-theory, and elliptic cohomology.- Fundamental groups and path lifting for algebraic varieties.- Cremona transformations of weighted projective planes, Zariski pairs, and rational cuspidal curves.- Normal reduction numbers of normal surface singularities.- Motivic Chern classes of cones.- Semicontinuity of Singularity Invariants in Families of Formal Power Series.- Lattices and correction terms.- Complex surface singularities with rational homology disk smoothings.- On Tjurina Transform and Resolution of Determinantal Singularities.- On the boundary of the Milnor fiber.