On the symmetry of Stokes regions of a simple singularity

1993 ◽  
Vol 296 (1) ◽  
pp. 481-491 ◽  
Author(s):  
Yu Jianming
Keyword(s):  
Simple Singularity

scholarly journals Matrix model for the total descendant potential of a simple singularity of type D

2021 ◽  
Vol 111 (4) ◽  
Author(s):  
Alexander Alexandrov ◽  
Todor Milanov
Keyword(s):  
Matrix Model ◽  
Simple Singularity ◽  
Type D

scholarly journals Degree counting for Toda system with simple singularity: One point blow up

2020 ◽  
Vol 268 (5) ◽  
pp. 2163-2209 ◽  
Author(s):  
Youngae Lee ◽  
Chang-Shou Lin ◽  
Wen Yang ◽  
Lei Zhang
Keyword(s):  
Blow Up ◽  
Simple Singularity ◽  
Toda System

scholarly journals Open Saito Theory for A and D Singularities

2020 ◽  
Author(s):  
Alexey Basalaev ◽  
Alexandr Buryak
Keyword(s):  
Parameter Space ◽  
Moduli Space ◽  
Homogeneous Polynomial ◽  
Coxeter Groups ◽  
Frobenius Manifold ◽  
Simple Singularity ◽  
Universal Unfolding ◽  
Wdvv Equations ◽  
Manifold Structure ◽  
Frobenius Manifolds

Abstract A well-known construction of B. Dubrovin and K. Saito endows the parameter space of a universal unfolding of a simple singularity with a Frobenius manifold structure. In our paper, we present a generalization of this construction for the singularities of types $A$ and $D$ that gives a solution of the open WDVV equations. For the $A$-singularity, the resulting solution describes the intersection numbers on the moduli space of $r$-spin disks, introduced recently in a work of the 2nd author, E. Clader and R. Tessler. In the 2nd part of the paper, we describe the space of homogeneous polynomial solutions of the open WDVV equations associated to the Frobenius manifolds of finite irreducible Coxeter groups.

The complement of the bifurcation variety of a simple singularity

1974 ◽  
Vol 23 (2) ◽  
pp. 105-116 ◽  
Author(s):  
Eduard Looijenga
Keyword(s):  
Simple Singularity

scholarly journals AND THE ARITHMETIC OF A FAMILY OF NON-HYPERELLIPTIC CURVES OF GENUS 3

2015 ◽  
Vol 3 ◽  
Author(s):  
JACK A. THORNE
Keyword(s):  
Rational Numbers ◽  
Hyperelliptic Curves ◽  
Simple Singularity ◽  
Integral Points ◽  
Average Size

We study the arithmetic of a family of non-hyperelliptic curves of genus 3 over the field$\mathbb{Q}$of rational numbers. These curves are the nearby fibers of the semi-universal deformation of a simple singularity of type$E_{6}$. We show that average size of the 2-Selmer sets of these curves is finite (if it exists). We use this to show that a positive proposition of these curves (when ordered by height) has integral points everywhere locally, but no integral points globally.

scholarly journals -constraints for the total descendant potential of a simple singularity

2013 ◽  
Vol 149 (5) ◽  
pp. 840-888 ◽  
Author(s):  
Bojko Bakalov ◽  
Todor Milanov
Keyword(s):  
Analytic Continuation ◽  
Vertex Algebra ◽  
Weight Vector ◽  
Simple Singularity ◽  
Moody Algebra ◽  
Basic Representation ◽  
Highest Weight ◽  
Finite Dimensional ◽  
Dynkin Diagrams ◽  
Twisted Representation

AbstractSimple, or Kleinian, singularities are classified by Dynkin diagrams of type $ADE$. Let $\mathfrak {g}$ be the corresponding finite-dimensional Lie algebra, and $W$ its Weyl group. The set of $\mathfrak {g}$-invariants in the basic representation of the affine Kac–Moody algebra $\hat {\mathfrak {g}}$ is known as a $\mathcal {W}$-algebra and is a subalgebra of the Heisenberg vertex algebra $\mathcal {F}$. Using period integrals, we construct an analytic continuation of the twisted representation of $\mathcal {F}$. Our construction yields a global object, which may be called a $W$-twisted representation of $\mathcal {F}$. Our main result is that the total descendant potential of the singularity, introduced by Givental, is a highest-weight vector for the $\mathcal {W}$-algebra.

Sign in / Sign up

Export Citation Format

Share Document