Orbifold Jacobian algebras for invertible polynomials
Alexey Basalaev, Atsushi Takahashi, and Elisabeth Werner
Journal of Singularities
volume 26 (2023), 92-127
Received: 16 October 2021. Received in revised form: 20 January 2023.
Abstract:
An important invariant of a polynomial f is its Jacobian algebra defined by its partial derivatives. Let f be invariant with respect to the action of a finite group of diagonal symmetries G. We axiomatically define an orbifold Jacobian Z/2Z-graded algebra for the pair (f,G) and show its existence and uniqueness in the case, when f is an invertible polynomial. In case when f defines an ADE singularity, we illustrate its geometric meaning.
Author(s) information:
Alexey Basalaev
Faculty of Mathematics
National Research University Higher School of Economics
Usacheva str., 6
119048 Moscow, Russian Federation
and
Skolkovo Institute of Science and Technology
Nobelya str., 3
121205 Moscow, Russian Federation
email: a.basalaev@skoltech.ru
Atsushi Takahashi
Department of Mathematics
Graduate School of Science
Osaka University
Toyonaka Osaka, 560-0043, Japan
email: takahashi@math.sci.osaka-u.ac.jp
Elisabeth Werner