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Twisted Koszul algebras of nonisolated hypersurface singularities

Sangwook Lee

Abstract

Given a hypersurface singularity (not necessarily isolated) with a finite abelian group action, we develop a method to define an explicit product structure on the twisted Koszul algebra (whose invariant subalgebra is the orbifold Koszul algebra).

Twisted Koszul algebras of nonisolated hypersurface singularities

Abstract

Given a hypersurface singularity (not necessarily isolated) with a finite abelian group action, we develop a method to define an explicit product structure on the twisted Koszul algebra (whose invariant subalgebra is the orbifold Koszul algebra).
Paper Structure (4 sections, 7 theorems, 97 equations, 1 figure)

This paper contains 4 sections, 7 theorems, 97 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Classification of closed morphisms of matrix factorizations
  4. An example in mirror symmetry

Key Result

Theorem A

Let $(W,G)$ be a diagonal orbifold LG model. Let $\Delta_1$ and $\Delta_h$ be Koszul matrix factorizations of the diagonal ideal and the $h$-twisted diagonal ideal respectively (for $h\in G$), of a polynomial Then we have a quasi-isomorphism of chain complexes

Figures (1)

  • Figure 1: The $\mathbb{Z}/2$-cover of $\mathbb{P}^1_{2,2,\infty}$ is the 2-punctured sphere, namely $T^* S^1$.

Theorems & Definitions (16)

  • Definition 1.1
  • Theorem A
  • Theorem B
  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Proposition 2.5
  • Theorem 3.1
  • proof
  • ...and 6 more