A unified mathematical approach to the calculation of numerical invariants and linear sheaves
The study of numerical invariants such as F-signatures and diagonal F-thresholds has recently revealed surprising links between commutative algebra and algebraic geometry. Supported by the Marie Skłodowska-Curie Actions programme, the PrIMes project combines these concepts with seemingly independent tools, including the cohomology of linear sheaves and the Lefschetz property. One of the main objectives is to establish recursive formulas for multiplication in the Han-Monsky ring. The results obtained contribute to the classification of the weak Lefschetz property in complete monomial intersections of several variables. Furthermore, PrIMes aims to study these invariants for square-free hypersurfaces with the aid of combinatorial structures.