arXiv subjects

Anton Rarovskii

Publications and source records attributed to Anton Rarovskii.

3 recordsLinked to original sources

arXiv2026

Open extension of a genus zero Hurwitz-Frobenius manifold

Every Dubrovin--Frobenius manifold provides a solution to the WDVV equation, that was initially formulated in the study of the moduli space of curves. During the last two decades special attention was given to the "open" version of the moduli space of curves. Its genus zero intersection theory is governed by the system of equations called open WDVV equation, that extends "classical" WDVV equation. In this note we study Dubrovin--Frobenius manifold structures on the Hurwitz spaces of genus zero. We construct explicitly the solutions to open WDVV equation for these Dubrovin--Frobenius manifolds and show that these solutions appear as the restriction of the Dubrovin--Frobenius structure to its discriminant.

math.AG↗

arXiv2025

Non-invertible quasihomogeneous singularities and their Landau-Ginzburg orbifolds

According to the classification of quasihomogeneus singularities, any polynomial $f$ defining such singularity has a decomposition $f = f_κ+ f_{add}$. The polynomial $f_κ$ is of the certain form while $f_{add}$ is only restricted by the condition that the singularity of $f$ should be isolated. The polynomial $f_{add}$ is zero if and only if $f$ is invertible, and in the non-invertible case $f_{add}$ is arbitrary complicated. In this paper we investigate all possible polynomials $f_{add}$ for a given non-invertible $f$. For a given $f_κ$ we introduce the specific small collection of monomials that build up $f_{add}$ such that the polynomial $f = f_κ+ f_{add}$ defines an isolated quasihomogeneus singularity. If $(f,\mathbb{Z}/2\mathbb{Z})$ is Landau-Ginzburg orbifold with such non-invertible polynomial $f$, we provide the quasihomogeneus polynomial $\bar{f}$ such that the orbifold equivalence $(f,\mathbb{Z}/2\mathbb{Z}) \sim (\bar{f}, \{id\})$ holds. We also give the explicit isomorphism between the corresponding Frobenius algebras.

math.AG↗

arXiv2025

Orbifold Saito theory of A and D type singularities

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.

math.AG↗