2025/07/10 by Basalaev, Alexey, Rarovskii, Anton
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2507.07609
Saito theory associates to an isolated singularity rich structure that plays an important role in mirror symmetry. In this note we construct Saito theory for A and D type Landau--Ginzburg orbifolds. Namely, for the pairs (f,G), where f defines an isolated singularity of A and D type and G is a group of symmetries of f. In total we consider five families of such pairs. In particular, we construct the orbifold versions of Brieskorn lattice and the Gauss--Manin connection computing them explicitly for the A and D type Landau--Ginzburg orbifolds.