Orbifold concepts in equivariant singularity theory

• Applicant: Professor Dr. Wolfgang Ebeling
• Subject Area: Mathematics
• Term: from 2017 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 346364045

Invariants of topological spaces and complex analytic varieties with actions of groups (say, finite ones) play an important role, in particular in topology, algebraic geometry and mathematical physics. The applicant and his coauthors S. M. Gusein-Zade and A. Takahashi also contributed to this research. In particular, they have described a number of symmetries between so called invertible polynomials with finite group symmetries (orbifold Landau-Ginzburg models). They have defined and studied some indices of invariant or equivariant vector fields and 1-forms and of their collections. The main objective of the project is a further development of the theory of invariants in the presence of a finite group action. The special focus will be on the orbifold setting and on orbifold type invariants. More precisely, it is planned to continue the search for symmetries between invariants of Berglund-Hübsch dual invertible polynomials (also with actions of possibly non-abelian dual groups), to study algebraic formulae for equivariant indices of 1-forms and vector fields, and to investigate orbifold analogues of the Milnor lattice. The proposed research also includes a study of generalizations of the McKay correspondence, of Chern characteristic numbers of orbifolds, and of the Orlik-Randell conjecture.

• DFG Programme: Research Grants