Orbifold Saito theory of A and D type singularities
Alexey Basalaev and Anton Rarovskii
Journal of Singularities
volume 30 (2026), 61-80
Received: 11 July 2025. In revised form: 3 April 2026
Abstract:
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.
Author(s) information:
Alexey Basalaev
Faculty of Mathematics
HSE University
Usacheva str., 6
119048 Moscow, Russian Federation
email: abasalaev@hse.ru
Anton Rarovskii
Faculty of Mathematics
HSE University
Usacheva str., 6
119048 Moscow, Russian Federation
and
Scientific School named after I.M. Krichever
Skolkovo Institute of Science and Technology
Bolshoy Boulevard 30 bld. 1
121205 Moscow, Russian Federation
email: aararovskiy@edu.hse.ru